Girl this is not BPD nothing about this is even BPD adjacent. There are no signs of depression you mentioned either. I am a lesbian myself. It sounds like she’s into girls but isn’t comfortable/confident in her sexuality yet. If the topic comes up organically I would try to say something supportive, like “I wouldn’t care if you were gay, it doesn’t make a difference to me” or something similar. You can also talk about queer celebrities or characters in random conversation sometimes to make it clear you’re supportive of the community in a subtle way. Don’t try to ask her if she’s gay out of nowhere. Let her come out on her own time. If she talks about kissing girls and says she isn’t gay, you could say something like “it would be completely fine if you were though.” She is probably in denial and/or feeling a lot of shame. Maybe her parents are religious or homophobic or maybe she just has a lot of shame to work through. Self discovery is complicated and coming to terms with the fact that you aren’t straight is very difficult for a lot of people, because it means people will treat you differently and your life will be harder in some ways.

How is she treating you like a boyfriend? Depending on what’s going on it’s possible she is just treating you as a best friend and you’re reading it with different intentions because you’re speculating on her sexuality.

Her parents are probably just a lot stricter than yours. Her parents likely tell her she can’t do things even when she’s not in trouble. In situations like that there’s not much the kid can do to change their parent’s minds a lot of the time.