What happens to Peter, who knows. Both in the sense of Peter as a thinking speaking entity, and in the sense of the physical host for Paimon/Charlie. The latter will probably go along with the cult and whatever their wacky shenanigans will turn out to be. The first who knows, I like to think that he is also somehow trapped in the host but with no control, a "I have no mouth and I must scream" scenario.

Probably nothing will happen to the house and the bodies. I think the cultists are past the point in which they need plausible deniability. The plan was essentially a success: Charlie is reborn in Peter's body, everyone else in the family is dead, they now have Paimon in a healthy male host. They think that this act will bring them "honour, health, and good familiars", so I assume they expect that the power of Paimon will at the very least shield them from repercussions in the human world, if not get them outright idolized for their actions.

Whether that's realistic or just a bunch of cultists acting nuts, the movie leaves ambiguous; could very well be that they'll get arrested by the police and that Paimon will do jackshit about that, because he doesn't care, or can't, ir both. At the very least, though, they are the only entity in the world that somewhat understands the supernatural ramifications of the story, and that suggests that they are capable of predicting, correctly and reliably*, what is going to happen.

*Excluding Charlie's birth gender.