It sounds like this girl has no sense of self. This is a major issue far beyond being a "copy cat." She may act superior, but her actions say exactly the oposite. I bet her acting like she's better than you is just a front to hide the fact that she feels far inferior. If she felt superior for real, then she wouldn't copy everything you do.

It is very clear from your post that this girl has a mental health issue and needs therapy. Whatever her issue is, it isn't something you can fix. She needs some help. You've known her for a long time and you said her door was already broken. Is there issues in her house? Her behavior is a 100% red flag that she's not well cared for, possibly talked down to, has no self-esteem or idea of self-value.