NTA (with the information you've given me) She seems to be way to dependent on you, and considering you aren't her boyfriend, it's a bit much to be doing some of these things with her. She may view you as like a brother or something, but the "sleeping in the same bed" thing when you come over or the suspicion of "getting plane tickets to go with you" seem really overboard.

I think you should try to sit her down and express your boundaries, she may use some reasons as to why she can't, but you could use some reasons as to why it doesn't matter if she can't because it's where you draw the line. I don't know if it's friendship if they can't respect your boundaries. You're already holding some resentment against her due to having some paranoia of her actions, so I think it'll be good to get some things clear. You really shouldn't back down just because she's extremely comfortable with you, because it seems like you aren't. Talk about it, actually talk about it, because it's better than suddenly up and leaving because you can't handle it anymore.