A few things - it's BS2 not WS2 (Ballistic Skill, rather than Weapon Skill), and a heavy bolter is S5, AP4.
During your deployment you may place a Gun Emplacement within your deployment zone. This emplacement has a twin-linked heavy bolter and may fire on its own at BS2. It is always in control of the owning player and may not be used by the enemy.
(Emphasis mine)
(1) Because the italics part suggests it can only not be manually fired by the enemy, and the bolded part suggests it's not
forced to use automatic fire, it is reasonable to conclude it
can be manually fired by your own models.
(2) There is a bit of debate whether they count as models - The common argument is that we are told by the rules that models will have a Unit Type, whilst a Gun Emplacement instead has a Terrain Type (Battlefield Debris), meaning it needed the special allowance to be shot at and attacked in combat. However, the rules use the term "model" slightly inconsistently (sometimes talking about "scenery models") so we don' really know.
The "Target Designator" upgrade also fails to list a time limit on how long it lasts. Given that it talks about "spending" the token, I'd guess it's effects only lasts a turn, but affects all shots from that model.
(3) Gun Emplacements cannot move (they are not Infantry, and have no other Unit Type to give them a movement value).
(4) We're not given any way to resolve it - the rules for zero-level characteristics don't explain what happens if you have an Initiative of 0. So it's either:
a) They wound automatically.
b) They wound on 2+ (taking the way the Strength / Toughness chart works and extending it).
c) It rolls to wound against Toughness (similar to how it rolls against a vehicle's Armour Value).
But ultimately we just don't know.
I know that hasn't been a great help, but there is a link to the
Heralds of Ruin Facebook group in the
FAQ file, and it suggests asking any questions there