As for the abortion scenario, there are lots of things to try to work out. First of all, does she have capacity to request and consent to a termination? This means does she understand what a termination involves, the risks it entails, and what the alternatives are? Does she legally fit the criteria for a termination (probably)? If she does, then she can consent to it herself - this is what the Fraser/Gillick guidelines are all about. If your personal beliefs mean that you do not feel able to refer her for abortion, you must direct her to someone who will. Regarding contraception afterwards, it's certainly worth thinking about but you generally only have 10 minutes, and she's already got a lot on her plate - so perhaps mention it, and then ask her to think about it and come back another time. Or, as I already mentioned, this can be covered by some termination services at the time.
You are right to raise the possibility of abuse/involvement of a significantly older party, and would have to try to explore that (treading very carefully as teenage girls are not the easiest to communicate with!) to make sure she's not in danger. If she is, then you have the right to breach confidentiality (though your first port of call would be your named contact for safeguarding children rather than the police or her mother) but this is something you should certainly seek advice from your seniors and your medical defence organisation before doing.
As for whether to tell the mother, if the girl has demonstrated that she is competent to make this decision for herself, then you have to respect her confidentiality, with the exception I've already described. You would encourage her to discuss it with her mother, or at least with somebody that she can trust, as terminations are scary things to go through on your own, but you cannot force her. When mother dearest starts screaming down the phone, you just have to explain politely that you are not able to discuss it with her.
Hope that helps - feel free to add anything or ask questions!