I think range is unlimited, but they can only travel within supply. Max. number of Gatlings is limited by AIP. Spawn rate is determined by faction intensity.
As far as I know, they do not require supply, nor do they take damage by jumping when out of supply.
Instead, they just have behavior limiters:
Hostile to all Gatlings can travel anywhere, but tend to wander around the systems near the Dyson Sphere looking for targets. As targets die, the Gatlings will move on to more distant systems.
Friendly Gatlings will wander through human controlled systems, only occasionally jumping 1 deep into AI territory as part of an attack on AI targets, or when travelling between human systems.
I know I've seen hostile Gatlings show up 20 or more jumps away from the Dyson sphere to attack (and kill) me. Thanks, Advanced Hybrids.
But, as Phoenix said, ever since the re-balance, Guardposts have been slaughtering the Gatlings, so they rarely survive long in AI space.