What did Charlie's aunt do?

The movie is fairly faithful to Stephen Chbosky's book, and in this reader's guide from shmoop (like Cliffs Notes or Spark Notes):

Charlie thinks about his mom's sister a lot. He even visits her grave, telling her secrets that he only shares in his letters. So why does he love and trust her so much? He thinks it's because she was one of the few people who bought him two gifts at the holidays—one for Christmas and one for his birthday, which was Christmas Eve. He thinks it's because she died in a car accident on Charlie's seventh birthday when she went to buy his birthday present. He thinks it's because he's guilty for her death...

Growing up, Aunt Helen was molested by a friend of the family. When she finally told her parents, they didn't believe her. They did nothing to stop it, and even continued inviting the man into their home. Eventually, Aunt Helen grew up and got away. But of course, the trauma stayed with her: "My aunt Helen drank a lot. My aunt Helen took drugs a lot. My aunt Helen had many problems with men and boys. […] She went to hospitals all the time" (2.13.9).

Victims of abuse often become abusers themselves. And of course, Aunt Helen goes on to molest Charlie. She took advantage of shy, quiet Charlie's love and trust. Charlie forgives her, but it has changed the course of his life forever.

Of best friend Michael Dobson:

As the novel opens, Charlie is still reeling from his best (and probably only) friend Michael's suicide. We never really get to know Charlie and Michael as a duo—all we know is that they went to a few football games and peeped inside their neighbors' windows. Seems like tame high school fun, but maybe Michael was window shopping for a new family.

We're pretty sure Michael exists to show Charlie how not to be. Even though Charlie eventually stops writing about Michael, the suicide still haunts him. When he experiences his own suicidal thoughts, he pleads with the reader, "I never wanted to. You have to believe me" (2.15.12), as if to say, I won't end up like Michael. I won't. Maybe he's trying hard to convince himself of that, too.

Michael is the only character in the book who gets a last name.

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.

He was most probably molested by his aunt and since he was only a child, those things were a bit cloudy to him. The events were apparently being reminded to him when some situations were done that by his new friends Sam and Patrick.

Sam told Charlie that she was molested by his dad's boss when she was 11. In that context, Charlie told her that his aunt was also molested (instead of him being molested by his aunt) and she turned out to be a nice person and that she was his favorite person. Obviously, Charlie was trying to make Sam not insecure about what happened to her. That she's not alone and everything was gonna be fine despite that event in her past. Even if Charlie changed his story, it reflected his experiences as well.

First of all, I'm pretty sure that's exactly what is implied, that his aunt abused him sexually. That is implied in the way Charlie gets the flashback of her rubbing his leg when Sam does the same to him. The situation is the same as it is motivated by the same feelings and not just out of mere friendship. This is only a slight hint, so it may be a bit confusing up until then. But it is later reinforced when Charlie is in the hospital and the doctor says:

Doctor: You said some things about her in your sleep.
Charlie: I don't care.
Doctor: If you want to get better, you have to.

And later it becomes pretty clear that there was something wrong with his aunt when he writes:

There were some very bad days and some unexpected beautiful days. The worst day was the time my doctor told my mom and dad what Aunt Helen did to me.

Now to the question why he still told Sam that his aunt was his favourite person. I think when he said that, he still believed that this is the very truth. Up until his actual suicide attempt after Sam shook up his memories, Charlie seemed to supress what his aunt did to him and was rather confused about his feelings for her. He only knew that he was a little boy and feeled a very strong emotional connection to his aunt, even if he doesn't completely know where this connection came from exactly or to which level it goes. I think at this point his aunt really still was his "favourite person".

It isn't until those strange memories about his aunt become clearer that he starts to realize the whole extent of his relationship to her and that this actually wasn't a good thing. And only then his love for her starts to change into maybe even wishing her dead. Though, I think even then he still is to a large degree confused about what to feel. He probably doesn't only feel guilty about her death (as she was about to fetch him his present when she died), but also about what he did (ingoring that he was only a victim to her) and also for maybe partly wishing her dead, knowing that it was wrong what she did but also not able to stop his feelings for her from one second to the other even though they're stained now. So he feels guilty for pretty much everything, what she did, what he did, that she died, that he maybe somehow wished her dead, that he should have wished her dead but couldn't and still can't, ... And this confusion and guilt is likely also the reason for his suicide attempt afterall. To say the least, his feelings are difficult at this moment.

As to his best friend killing himself, that isn't alluded to much and doesn't seem related to the matter of his aunt at all. It is another aspect of his troubled past, and maybe also an aspect to stress his own difficult mental state and the possible future he might have been looking toward.