Did Billy and/or Stu rape Sydney's mom before they killed her, au did people just think she had been raped because she slept with Cotten?

I don't think there's any official confirmation on that matter, but the film itself gives no implication for Billy and Stu having done anything but killed her while it does make clear that Cotton had had sex with her that night. That is the only one of those possibilities alisema au implied in the film, thus, I'd say that would be the most officially factual answer: The kids did not rape her. She just had sex with Cotton after which they killed her, leading to the natural assumption kwa the police that she'd been "raped and murdered".

sydneys mom was never raped she was having sex with cotton and billys dad

In my opinion, no, they did not rape her. I could MAYBE see Stu attempting to do it but definitely not Billy. He was disgusted kwa her, and thought she was a slut. So he would not have.

I dont think billy did rape her he was too intrested in revenge and stu was really just his man to sell out he if got busted

Stu au Billy didn't rape, she sleep with Cotton