So we've got three Rogue Traders.
All are HQ, and all share the Astra Cartogaphica trait, meaning you could make a detachment with them, but since no other unit in the game has the Astra Cartographica trait, it would have to be a supreme command detachment.
The Rogue Trader Elucia Vhane actually has a retinue though. Her Voidsmen are a troops choice, and she's got 3 elite character models, so you can field them as a Vanguard.
If you do, however, you lose your capacity to field the other two Rogue Traders, because there's no other model to make up the supreme command.
As for Inquisitors, you can either attach individual Inquisitors to other Imperial detachments, or field Inquisition attachments, but you can't do both.
In terms of attaching Inquisitors, the become "slotless" and they don't interfere with army purity or detachment purity rules. You may have to put up with people who interpret the rules to mean that you can only include an Inquisitor in one of your detachments- honestly, the rule is vague enough to support either interpretation.
If you include Inquisition detachments, it may interfere with army purity rules- again, it's somewhat ambiguous, although in this case, I do think interference with army purity is the more obvious interpretation, though it pains me to admit it.
Inquisition has no troops choices, and you can only include one Inquisitor in each detachment, which once again limits you to Vanguard detachments. For elites, you have Jokaero, Acolytes and Demonhosts.
There are four named Inquisitors, you could take three of each Ordo, and then three more Malleus in Terminator Armour, meaning a maximum of 16 Inquisition Vanguards. Plus either a Euclidean Starstrider Vanguard or an Astra Cartographica Supreme Command, but not both.
As for Assassins, I don't have the rules for them, but I believe you pay CP before battle to take a detachment which includes up to one model from each Temple, and the detachment doesn't interfere with army purity.
It's also worth mentioning that both Inquisitors and Rogue Traders can ride any Imperial Transport, but neither have transports in their own list. I think Forgeworld books have a Land Raider entry under Inquisition, but Rogue Traders have none.
I full expect an Imperial Agents Codex, and this would be a good year for it- PA is just begging for Astra Telepathica updates. If we get that dex, it will likely allow the Inquisition to grant their Ordo keyword to troops from other Imperial forces. What I would personally like to see is an option for Inquisitors to grant their Ordo keyword to their Chambers Militant.
Of course, now that every army is getting mono faction bonuses, it would actually be better for GW to just clarify that Inquisitorial Vanguards don't break army purity- that way you could field as many Vanguards as you wanted; all of the members of each Vanguard get Quarry, and the rest of the army keeps it's doctrine.
Souping with another army doesn't have to make the army feel less Inquisitorial or Rogue Traderesque. I keep it to the old school Chamber Militant idea- so much so that I actually bought the GK dex + PA and the Deathwatch dex specifically for the purpose of fielding them with the Inquisition.