Question: Is it me, or is Carrie's mother smiling when she gets stabbed multiple times by Carrie?
Answer: She was also crucified, which makes her feel connected to Jesus.
Answer: I think for somebody as repressed as Carrie's mother even something like physical pain is a kind of release (her moans sound sexual to me). Also, remember the mother talking about enjoying Carrie's father touching her? "Hands all over me", there could be a parallel there.
I agree – it almost seemed like she was having an orgasm, or close to it, during her death throes.
Question: Why did they change her name from Rita Desjardin, in the book, to Miss Collins?
Answer: The only answer I could find online was that it was changed simply because "Miss Collins" was easier to pronounce/remember. It's also worth noting that it's really not all that uncommon for movie adaptations to alter and rename characters. Especially supporting characters. Given there are some other changes to the character in the movie, renaming her could have also been a way to distance her more from the character in the original book.
Question: Why do Chris and her friends bully Carrie? She's never done anything to them and I've read the book which also provides no answers.
Answer: Bullying doesn't have anything to do with whether or not someone did anything to someone else. Bullies zero in on people they know are emotionally weaker and less able to defend themselves. Carrie was extremely shy, awkward, naive, etc. These are traits that bullies tend to exploit for their own amusement and to make themselves feel superior.
Question: I believe that Carrie did not actually die at the end of the film and is waiting to torment Sue and whoever else messes with her. Anyone adhere to this?
Answer: That was always the impression I got until the sequel was released in 1999 (The Rage: Carrie 2) that made it clear Carrie White was definitively dead.
So her grabbing her arm, what was the purpose for that?
It was a nightmare, never happened, it was just Sue's imagination.
Answer: Her grabbing her arm was a guilt ridden nightmare that Sue had.
Answer: My feeling is that being so fundamentally religious that she was almost happy to finally die, and meet God as she believed.