1. How intelligent is a 3rd Generation 'Stealer'? Human? Subhuman? Can they use tools/weapons/operate heavy machinery?
Yes, but they will experience great difficulty interacting with humans outside the cult.
2. If the Primarch is killed as well as the Magus does the cult scatter? Do they rebuild?
It's Patriarch you want - Primarch is a *very* different thing. They would likely scatter, and are unlikely to rebuild unless there's another Magus or 2nd Generation still knocking around.
3. How potent is the 'Brood Mind'? What I mean is, can other psykers detect it?
Well, it's potent enough that the Tyranids can detect it from far away, so it seems for a planet not to notice it straight away must require some masking on the part of the Patriarch and/or Magus. It's certainly possible for other psykers to detect it - it'll be a weaker version of the psychic blockade that follows the Tyranids, which causes psykers nightmares beforehand, an oppressive and restrictive feeling on the battlefield, and creates warp storms too.

 Warmaster_Horace wrote:
One of my buddies is a real stickler for fluff, and while I don't mind taking liberties with the material, I'd rather avoid anything too eye-rolling. ("You are greeted by a tap-dancing Black Templar and his talking Hormagaunt!")

So another question would be: If members of the cult are being mind controlled, do they regain their 'humanity' when that mind control ends?

For the starting scenarios the PC's would be investigating sporadic, but growing psychic activity in the lower rungs of a Hive City. Twenty years previous, these same lower rungs saw the emergence of a powerful psyker and small retinue of mutant followers (Genestealers + Magus) but were put down in such spetacular fashion (whole sector collapsed) that they were never properly identified.

 dementedwombat wrote:
Also I now desperately want to see someone make a cartoon about the tap-dancing Black Templar and his buddy the singing hormagaunt who backs him up on piano!