In the show South Park, Stan/Kyle roughly represent the ideals the writers see themselves as striving for, while Cartman is who they subconsciously want to be
I don’t need to read a book to make me okay with chopping someone’s family up and feeding them to the surviving member as a form of revenge, thanks tho.
Stan and Kyle are indeed based on Trey and Matt, as well as their families. That've stated that much. But I don't really see how you came to the second hypothesis. I've never seen any indication of that.
Sadly, I don't think so. They initally gave the families the names of their family members and in the first two seasons most of Shelly's behaviour is actually based on what Trey's sister did to him.
But during those seasons the parents where mostly thought of as background characters. When they expanded the roles of the parents in the show, they didn't really base their character on their parents anymore. Like Matt's mom never went rouge like in the movie. And when Randy becaome a main character he pretty much only shared Trey's Dad's name, not much more.