After looking through the Thousand Sons legion list and comparing them with a few other legions, I found them to be... underwhelming.
Now, I haven't played this game mode, but from my experiences with 8th edition Warhammer and its balancing (which I believe you are attempting to emulate), I came up with a few issues regarding the Thousand Sons unit list.
Do take this with a grain of salt, as this may be some of my internal biases speaking.

Regarding legion traits:
• Prosperine Lore: If a Thousand Sons Character is selected to be the Warlord, they must be a Psyker (or take the Psyker upgrade,
detailed below in ‘Legion Wargear’). In this case, the Warlord must be the Thousand Sons Character with the highest Leadership
characteristic in the detachment. Thousand Sons Praetors must always take the Psyker upgrade.

I understand the purpose of this rule, and it is very fluffy. However, it simply adds more restrictions and gives absolutely no benefit to the Legion as a whole.

I propose it be changed to this:
• Prosperine Lore: If a Thousand Sons Character is selected to be the Warlord, they must be a Psyker (or take the Psyker upgrade,
detailed below in ‘Legion Wargear’). In this case, the Warlord must be the Thousand Sons Character with the highest Leadership
characteristic in the detachment. Thousand Sons Praetors must always take the Psyker upgrade. All Thousand Sons Character Psykers
may take Arcane Litanies for 0 pts, and all Thousand Sons units can add 1 to their attempts to cast powers from their cult discipline.

This would reflect their mastery of the warp gained from experience, as well as have this rule grant some actual benefit for a Thousand Sons
army instead of just adding more restrictions.

• Cult Arcana: Units with this ability gain the <Cult> keyword. With the exception of HQ choices, compulsory choices in a Thousand
Sons Detachment must choose the same <Cult> as the Warlord (if possible). The five cults and their respective abilities are listed here:
• Athanean: Enemy Psykers suffer -1 to attempts to manifest psychic powers within 18” of models from the Athenaean cult.
This is simply an improved Shadow in the Warp from the Tyranids, and even then it would not be considered useful as a subfaction attribute
in constructed 8th edition. This is compounded by their poor psychic selections, the only generally useful power being Mass Hypnosis.

• Corvidae: Models from the Corvidae cult can re-roll hit rolls of 1 in Shooting phase, if they were stationary in the Movement phase.
Again, this is simply a worse version of the Dark Angels subfaction trait. This does not make sense, nor is it really lore-friendly.
The same argument for the Athanean cult applies to this as well. It is weaker than a standard WH40k 8th edition subfaction trait, and not
even a particularly good one at that. The Corvidae are seers, and the "reroll of 1 if they did not move" does not make sense with their lore.

• Pavoni: Models from the Pavoni cult can re-roll failed charge rolls.
Once more, this is simply a worse subfaction attribute (Craftworld Eldar's Saim'Hann trait includes this, along with the added bonus that BIKERs
ignore the penalty to move and shoot.) It also does not really make sense in the lore either, as the Pavoni have mastered the art of Biomancy.

• Pyrae: Models from the Pyrae cult are equipped with Psychic flames.
This is a truly unique cult attribute, and one of the two attributes that I consider to be truly unique and fitting of Thousand Sons lore. Kudos
to you.

• Raptora: Models from the Raptora cult have a 6+ invulnerable save, or add 1 to their existing invulnerable save.
Again, this is a unique and fitting ability for the Raptora cult. This ability is very fluffy, and quite balanced.

Kudos to you for including each Prosperine cult as a core gameplay mechanic for the Thousand Sons. However, each bonus provided is incredibly
underwhelming, especially considering how restrictive the "same cult as Warlord" clause is, added with the fact that this is the only real
benefit gained by Thousand Sons for their legion rules.

I propose it be changed to this:

• Cult Arcana: Units with this ability gain the <Cult> keyword. With the exception of HQ choices, compulsory choices in a Thousand
Sons Detachment must share the same <Cult> keyword (if possible). The five cults and their respective abilities are listed here:

• Athanean: Models from the Athanean cult automatically pass Morale tests (do not roll the dice.)
This is reflective of the 7th edition HH attribute granting immunity to Fear and Adamantium Will. This helps with Signs and Portents.

• Corvidae: Whenever a model from the Corvidae cult loses a wound, roll a dice. on a 6+, the wound is not lost.
This is reminiscent of Ulthwe's Foresight of the Damned trait, which is the same as the proposed Corvidae trait. This reflects the
uncanny prescience the Corvidae have, and offer a decent attribute that is universally useful.

• Pavoni: Models from the Pavoni cult add 1 to their Movement characteristic and can add 1" to the distance they can Advance.
Again, somewhat copied from the 7th edition HH trait where they can run and sweeping advance with +1 to the roll. It tones that down
somewhat, though it's far from overpowered. I contemplated adding a mutable +1 S, T, or A buff, but that seemed way too overpowered.

• Pyrae: Models from the Pyrae cult are equipped with Psychic flames.
No change needed here, though I do propose a change to the psychic flames weapon itself:
Psychic Flames: Range Type S AP D Abilities
8" Pistol 1 5 0 1 This weapon automatically hits its target
This would allow the power to scale with squad size, which would make the Axis of Dissolution's requirement of maximum Troops unit sizes
much less of a disadvantage. It also lessens the wordiness and complexity of the weapon itself, and makes more sense, as a unit combining its
psychic strength makes more sense than only allowing a single model to use it.

• Raptora: Models from the Raptora cult have a 6+ invulnerable save, or add 1 to their existing invulnerable save.
No change needed here, but note that it would allow Sekhmet Terminator Cabals to gain a 2+ Invulnerable save (native 4++
from Cataphractii Armour, coupled with +1 from Raptora Cult and +1 from Psychic Barrier). Overall, note that the Raptora
Cult right now is by far the strongest cult, having the best psychic selections (Warptime, Weaver of Fates, and Miasma of Pestilence
are their counterparts in WH40k 8th edition and they are all fantastic psychic powers.) Perhaps add a "To a maximum of 3+" clause
in there.

• Signs & Portents: Each time a unit with this trait suffers a wound as a result of Perils of the Warp, all friendly Thousand Sons Astartes
suffer -1 to their Leadership when taking Morale tests for the rest of that battle round. In addition, if all Thousand Sons Characters in
the army are slain, all friendly Thousand Sons Astartes suffer -1 to their Leadership when taking Morale tests for the rest of the game.
This is a very strong disadvantage, making each Perils proc force a -d3 ld penalty on Thousand Sons. However, considering the proposed upsides,
especially the Athenean cult revamp, this disadvantage is manageable (especially with Litanies).

Regarding Legion Wargear:
Thousand Sons models have access to the following wargear:
• A Character (without the Psyker keyword), Legion Veteran Tactical Squads and Legion Terminator Squads can take the Psyker upgrade.
• Any Psyker Character can replace their chainsword with a force sword, force axe or force stave.
• Any Psyker Character can take arcane litanies.
• Any Character, Veteran Tactcal Squad, Legion Terminator Squad or Tactical Support Squad can take Asphyx shells.
• Any Contemptor Dreadnought can take the Osirion upgrade.
• Any model can replace it’s Plasma cannon/Heavy plasma cannon with a Ætherfire cannon.
• In addition, a model in a Thousand Sons detachment can choose the Luminiferous Resonator instead of a relic from the Legiones
Astartes list.

I would advocate to allow ALL Thousand Sons INFANTRY units to take the Psyker upgrade, to reflect the ubiquity of psychic mutations
in the Thousand Sons legion. This would not be TOO game-breaking, but it would be a fluffy bonus.

I would then also advocate to allow any Thousand Sons INFANTRY unit to take Arcane Litanies, to make the Signs and Portents
legion trait more manageable.

As of now, the Luminiferous Resonator relic is quite weak. It also does not really reflect the psychic focus of the legion. Thus,
I propose it be replaced with this:
The Book of Magnus: PSYKERS only. This character knows 1 additional psychic power, generated from any cult discipline, and can
attempt to cast 1 additional power per psychic phase.
This is a useful artefact for any point value, because it adds some psychic versatility. It essentially lets 1 character take on
the psychic responsibility of two without having to buy another one for another power you want. This may be a little powerful, but
I feel that it will not be too overpowering, as a Praetor equipped with it will be able to cast 3 and deny 2 powers, on par with
Ahriman. It may be used to allow players to create a Magister Templi (which you do not currently have rules for). Thus, the pts value
of this artefact may be equated to roughly 20 or 30 pts.

Regarding the Thousand Sons Warlord Trait:
A Thousand Sons Warlord may choose the following Warlord trait:
• Psychic Exemplar: The Warlord may add 1 to any Psychic tests made to manifest powers from their Cult Discipline. Any rolls of 12+
count as Perils of the Warp.
This does not really make sense. The "result of 12+ still triggers Perils" clause is shared by Ork Weirdboyz. This is not lore-friendly.
Why would a Psychic Exemplar be unable to control their prodigious power? Additionally, this makes their Covenant of Sorcerers stratagem
much more dangerous when used on this warlord, as, RAW, the +2 bonus will vastly increase the chance of triggering Perils, and S&P, as well.

Thus, I propose it be changed to this:
• Psychic Exemplar: The Warlord may add 1 to any Psychic tests made to manifest powers from their Cult Discipline.

Regarding the Legion Rites of war:
The Axis of Dissolution
This rite may only be taken by a Patrol or Battalion detachment.
Advantages:
• The Alembic of Adamant: Thousand Sons units in this detachment ignore Morale tests when they are within 6” of an objective.
Due to the Athanean Cult's proposed rework making this obsolete, I will suggest a change.
• The Caustic of Grace: Thousand Sons units in this detachment hit on 5+ when firing overwatch.
• The Transition of Vitriol: Thousand Sons units in this detachment may re-roll failed hit and wound rolls against enemy units
which Fell Back in their previous turn.
Drawbacks:
• This rite may only be taken by a Patrol or Battalion detachment.
• All Troops choices in this detachment must be at the maximum possible unit size.
• This detachment may not have more units with the Vehicle keyword (except Dreadnoughts) than it has with the Infantry
keyword.

All in all, a fluffy and solid detachment, especially with the proposed Athanean and Cult Abilities rework. Every cult has
its unique strengths that fit into this Rite. I propose the Alembic of Adamant be changed to this:
THOUSAND SONS INFANTRY units in this detachment receive the benefit of cover when they are wholly within 6" of an objective.

This grants some great protection while still being vulnerable to Phosphor weaponry and mortal wounds, as well as cover-
ignoring abilities and psychic powers.

The Guard of the Crimson King
This rite may only be taken by a Vanguard detachment.
Advantages:
• Wreathed in Lightning, They Rend the Veil: Thousand Sons Terminator and Character units gain the Teleport Assault ability
and, when they are set up on the board, can re-roll failed invulnerable saves of 1 until their next turn.
This potentially allows another iteration of the Screamerstar, with 2++ rerollable Sekhmet Cabals. You may want to look into this.
• Teleport Assault: During deployment, you can set up this unit in the teleportarium chamber instead of placing it on the battlefield.
At the end of any of your Movement phases this unit can perform a teleport assault - set it up anywhere on the battlefield that is more
than 9” away from any enemy models.
• The Initiates of the Scarab: Sekhmet Cabals must be the compulsory Elites choices in this detachment.
• The Bidding of the Crimson King: Magnus the Red may be selected as a HQ choice in this detachment.
Drawbacks:
• This rite may only be taken by a Vanguard detachment.
• The Warlord must be in this detachment, and that Warlord must either be Magnus the Red, Ahzek Ahriman or a Thousand Sons
Praetor.
• This detachment may not have more units with the Vehicle keyword than it has with the Astartes keyword.
• Your army may not include a Fortification Network detachment.
• Your army may not include any units without the Thousand Sons keyword.
I am happy with how this Rite is, both fluff wise and balance wise. No changes needed, except the possible 2++ rerollable cheese.

Regarding the Khenetai Blade Cabals:
Each Khenetai Blade costs 21 pts. Coupled with the 10-pt cost of their Force Blades, this brings the combined cost for 1 model up to
31 pts per model. This is *very overpriced.*
Compare them to a Dark Eldar Incubus, which costs 16 pts combined (half as much):
Model: M WS BS S T W A Ld Sv
Incubus: 7" 3+ 3+ 3 3 1 3 7 3+
Blade: 6" 2+ 3+ 4 4 1 2 7 3+

Compare their weapons:
Weapon (pt cost) S AP D Abilities
Klaive (4 pts): +1 -3 1 -
Force Blades (10 pts: User -3 d3 -

Compare Abilities:
Incubi:
Power from Pain (6+ FnP Turn 1, add reroll failed charges Turn 2, +1 to hit in melee Turn 3, immune to Morale Turn 4, -1 Ld 6" aura Turn 5)
Tormentors (If a morale test is failed within 6", 1 extra model flees)

Khenetai Blades:
Mindsong of Blades
Psyker (probably best being Burning Blades from the Pyrae discipline)

In summary:
Incubi are faster, slightly less tough, have more attacks, comparable abilities, and cost half as much as Khenetai Blades.
They perform equally well against all single-wound targets, though the Blades come into their own against multi-wound targets, though
they will wound most of them on a 5+ or 6+ (4+ or 5+ with Burning Blades active). The d3 damage will then allow them to deal double
damage Incubi would do. However, this is not really their niche. You're supposed to throw Terminators to crack vehicles and heavy infantry
in melee, not a dual sword unit, which seems much more offensively focused.

From a points standpoint, Force Blades are Force Swords thatcost 2 additional points for some reason. Thus, I propose they be changed to 8 pts (from 10) for consistency. Mindwong of Blades is fantastic,
though the +2 Attacks effect is required for this unit to perform even remotely on par with Incubi. And, this makes them very susceptible to
Morale and ranged fire. Thus, I propose their base profile be raised to 3 Attacks (reflecting their dual weapons or martial mastery), and the
bonus granted by 9-10 models reduced to +1 Attack. In addition, I propose the pts cost of a Khenetai Blade be lowered to 18 pts (from 21), making
the effective pt cost of a Khenetai Blade 26 pts (from 31), a minimal unit to 130 pts (from 155), and a maximum unit to 260 pts (from 310 pts).
I propose lowering the +1 Attack threshhold given by Mindsong of Blades to 7-10 (from 9-10) to lower the required risk of running large squads of Blades.
This will put their performance (and cost) roughly on par with that of Khorne Berzerkers in WH40k standard 8th edition. The issue of d3 damage weapons still
stands, however, and thus there is the option for Force Blades to grant S:+1 instead of S:User, and keep their points cost at 10, though this would
shift their focus from "storm of blades" tarpit crackers to "storm of blades" transport and tank crackers.

Regarding more Wargear:
Arcane Litanies are overpriced. Chaos Space Marine Sorcerers may take Familiars for 10 pts, which grants a flat +1 to cast psychic powers. Thus,
I propose Arcane Litanies allow the reroll of 1 dice per psychic phase, or have their price decreased to 5 pts.

I propose a new wargear be added: Tutelaries. Tutelaries are small daemon familiars that Thousand Sons sorcerers often had, increasing their psychic
powers, though they turned on the Thousand Sons during the Burning of Prospero, overloading them with chaos energy until they became Chaos Spawn.
Thus, I propose this new wargear be added:
Tutelary (8 pts): may add 1 to any Psychic tests made to manifest powers from their Cult Discipline. Any rolls of 12+
count as Perils of the Warp.
This is strong, fluffy, and balanced (it is 2 pts cheaper than the chaos familiar option because of the added risk.)

Asphyx Shells, I believe, are priced well.

I feel the Aetherfire Cannon is a little weak for the price point, being a slightly stronger unsupercharged Plasmagun, for 8 more points.
I propose it be changed to either of the following profiles:
Range Type S AP D Abilities
36" Heavy 3 7 -3 d3 -
24" Assault 3 7 -3 d3 -
This makes it worth roughly 1.5 rapidfiring plasmaguns, reflective of its cost. The Heavy version would basically make it a better, higher
priced Autocannon. The Assault version would simply make it an improved plasmagun for deleting heavy infantry.

Regarding Ahzek Ahriman:
I was, quite frankly, disappointed with the Thousand Sons characters' casting abilities. Ahriman in 8th edition gets 3 casts and denies, with +1 to all of them.
This should be his casting statline in 8th edition HH (add 1 deny as well as a tutelary), with his price increased
to 155 pts to compensate.

I very much like Magistus Amon, though I propose adding a tutelary to his abilities and increasing his price from 162 pts to 170 pts.

Similarly, I am rather disappointed with Magnus' psychic capabilities. Like his standard WH40k 8th edition iteration, he should get
+2 base to cast from Arch Sorceror, and though he should be able to cast and deny four powers per psychic phase, the accompanying price
increase would bring it out of line with the powerlevel of other Primarchs. Thus, I suggest Arch Sorceror be modified to grant +2 to cast
and deny, while increasing his denial range to 30". His price should be raised to 470 pts (from 460) accordingly.

Regarding Sekhmet Cabals:
A Sekhmet Terminator's base cost is 40 pts. This, coupled with the Force Weapon cost of 8 pts, puts them at an astonishing 48 pts per model.
They are criminally overpriced (once the 2++ rerollable cheese is addressed). To put this in perspective, Thunder Hammer/Storm Shield terminators
in regular WH40k 8th edition cost less, while they have a 3++ invuln and Sx2 weapons with AP-3 and a flat 3 damage, with 1 less wound.
I would strongly suggest reducing their base points cost to 33 pts, making a Power Fist Sekhmet Terminator 45 pts. Compared with the Adeptus Mechanicus
Cybernetica Datasmith model, it would be 1 pt more expensive, though with a comparable ranged weapon and 1 less wound, though with psyker capabilities.
A fair price.

I very much like the design of Ammitara Intercessors, I do not believe a change is necessary.

- The Legion Trait 'A Talent For Murder' should probably specify that you need more friendly INFANTRY models than enemy INFANTRY models. I played against a guy who brought a load of tanks, and because they were technically just one model, I was able to take them out with my infantry a load easier than I believe I should have. The second game I played, I made sure to adjust that myself, but I never ended up getting into CC with any vehicles. However, the official rules specify infantry, so I thought it might be a good idea to carry that over.
- Trophies of Judgement have two rules listings, one saying enemy units that have taken casualties must take their moral at a -1, and the other saying units within 3" are -1Ld. That's something that I feel needs clearing up.
- The Horror Cult RoW doesn't really give any benefits that I would personally deem worth it. You are restricted to having to bring Raptors, having to be traitors, having to charge, and not allowed any fortifications/other Legions etc. The only real benefit is the 3 CP rather than 1, and maybe the Trophies of Judgement (I don't know if the Kharybdis is any good, as I don't have one myself). I don't really know what else to do to this RoW to make it more worth is bar potentially raising the CP, which brings me to my next point.
- I feel that the CP for both RoWs (and probably all RoW for all Legions, although I haven't had a proper look) should maybe be increased to 4 or 5, similar to the Battalion detachment. With the Terror Assault, I felt very limited with the 6CP, which in both games were delegated to just keeping the Night Raider stratagem going. Alternatively, I feel the RoW should change the unit's type from Elite or Fast Attack to Troop, so people can simply take the Battalion Detachment.
- The Night Raider stratagem is really quite powerful, making my Night Lords a load more survivable than normal. To counter this, you could make the cost of the stratagem be the same as the game turn, so by turn 3 it's 3CP, turn 4 it's 4CP, etc. This would counter the power, be similar to the official rules (second turn night fighting on a 2+, third turn on a 4+ etc), and make for an interesting stratagem.
- The first part of the Terror Squad's 'Executioners' ability is very powerful. I feel it should emulate the official rules, and be re-rolls of 1s against Infantry rather than re-rolls of fails. Their 'Concealed Positions' ability also seems very strong on paper, but so far it hasn't been too overpowering in the games I've played.
- Personally I think the Night Raptors should be WS 2+, but loose the re-roll 1s, as that is again more similar to the official rules. However, I have not properly used them in a game, and I realise there may be some combinations that makes that too powerful (eg then and Curze might be very strong if they hit on 2+), so feel free to ignore this.
- Sevatar's 'Master of the Atrementar' ability should maybe be increased to 6", as it can be very difficult to set up an entire squad within 3", especially if the squad is at max size. I also think the '1" closer' thing doesn't feel right for the rule, but I can't think of a more suitable alternative that isn't OP, so I guess it's as good as.
- Talking about Sevatar, I personally think his Psychic power should be what it is in the official rules; re-rolling hits, wounds, and saving throws. However, this again might end up being too powerful in your eyes, so feel free to ignore.
- Finally, I think Curze should have the 'Jump Pack Assault' ability that all Jump Pack Infantry units have, again to simply carry over some of the rules from the official rules.