Don't know if you want to, but it might help to express your concerns to her, a gentle but honest confrontation. If you can't do this, I think I would keep away. She sounds troubled and insecure, some of her behaviors may be impulsive, she starts something then withdraws, maybe upset with herself for her actions. The question really is, perhaps, what do you want? If it freaks you out and you do not want a relationship with her then disengage and be civil but not friendly or inviting.....and don't be afraid, if she invites herself and this is a problem, to let her know (privately) that it is not OK to do this.