How Did Emily Not Know About Charlie Really ? (spoilers)

Of course Emily knew that Charlie was an alternate personality of her father. That was why she didn't know how to respond when her father (when he was "himself") confronted her about Charlie. She also knew that Charlie resented her father. I once saw a documentary on people with multiple personality disorders. One had a dog, and he had taught the dog that it wasn't allowed to be on the couch. However, the dog could sense when he shifted to a different personality (a child-like one) - that personality didn't mind the dog being on the couch, so up on the couch it jumped. Of course, dogs and children are two different things, but Emily's father pretty much isolates her by taking her out of her normal environment after the tragedy - leaving her with no help to interpret her father's multiple personality disorder. Charlie probably manipulated her a great deal as well.

Regarding your other question, nothing suggests that Charlie abused Emily physically, but he most certainly did start to abuse her mentally - "I don't wanna play with Charlie anymore".

Okay, I'm going to make this real simple for you: she's. ~9. years. old.

I'm not psycho, just a little loopy.
*~me~*

I, too, found it hard to believe that she wouldn't say Dad and Charlie were the same person. As far as I could tell, DeNiro wore the same clothes and had the same hair for both personas--the only thing different was the facial expression, and possibly the voice was a little different. Anyone would know it was the same person. Too preposterous, but still an engrossing movie.

Because I bet the whole time she was having fun and playing games with Charlie at the start, he was telling her "don't tell your father". Then as he got more violent and scary (see: the scene where Charlie scares her and possibly does something to her when the lights go out during a game of hide & seek) she becomes too afraid to tell her father. Who knows, if she said, "Dad, you're Charlie" Charlie could come out and attack her. They live alone too, so she had limited people she felt she could turn to. She had to protect herself.

She DID know.

I think she knew shortly after moving, and had a basic understanding enough to know that if she tried to force the understanding on him, things would go even worse for her than if he came to his own conclusions. It's why she was weird to Elizabeth, to chase her away, to try to protect her