Yes. The belief in Satan presupposes belief in God. They believe that we were all created by God, but that he abandoned us because we were too flawed. The Illuminati worldview has a very negative opinion of humanity. They believe Satan has promised them transcendence to a higher form in exchange for servitude to him.

One would think they would have to. They could potentially be LaVeyan which is really more a philosophy than an actual religion from my understanding, but that's unlikely as they're presumed to preform rituals. I don't really follow the whole Illuminati idea myself, but it's interesting food for though I suppose Edit: Now that I think of it, LeVayan s Satanism is a fairly recent thing. If the Illuminati is real and is as old as people say, then it's not likely they are LeVayan. So in short, yeah, they probably believe in God

LaVey is bullshit.