>>1 So would you say she mostly only hangs with you at school? If so I would say that's not actually a good sign. It kinda says something if she make little effort to spend time with you outside of school but is shown to be perfectly capable of going to hang out with other people.
I wouldn't say she doesn't wish to be your friend but it's entirely possible that she doesn't view you as a go to friend but possibly as just a side friend. Or maybe she's unsure if you want to hang out with her outside of school. Maybe she's worried about annoying you?
Maybe the best thing to do would be for you to try and invite her to do something.