I will quickly give my take on your question:
Firstly, I would say that it is not the only central theme - friendship for one, I think is much more central. But yes, both child abuse, suicide and mental illness are central themes as well.
As the other post mentioned, the aunt, gave him two presents on his birthday, and therefore actually made a big deal about his special day, which is important for such young children. My guess is that she in other manners too paid much attention to him, which probably was not done to many others, as Charlie was a quiet child.
"If so, and he actually wished her death, why did he say to Sam that she (his aunt) was his favorite person ever?"
I think that when he was in the spot, he wished her dead, because he knew that the attention he was getting was wrong, and he didn't know how to stop it. As he says, he is afraid that he killed her, since it was his birthday present she went out to get. This must have caused him a lot of guilt, which is why he keeps telling everyone that she was his favorite person. He probably feels that this is the least he can do to honor her memory.
Now I have only seen the movie. The book might clarify things much more.