I realise it's a bit off-topic, but from a purely academic perspective do you think it's wise to offer tuition for an exam you've only recently passed yourself? I've heard that a good rule of thumb is to only tutor up to an education "stage" one step lower than the one you've completed - so in your case that would take you up to GCSE. Unless of course you did absolutely brilliantly at the A level and are totally sure you understand 100% of the syllabus - because if there's even one topic within it that you haven't thoroughly mastered, sooner or later you'll end up transmitting your own misunderstanding to students, which is embarrassing once you realise that that's what you've done.
I think I can speak with a bit of experience here, as a maths tutor of some years myself; a few months ago I was invited to tutor a girl of the same school year as your student, and as we began her parents explained that she'd recently had a tutor who had turned out not to know his subject well enough, so they'd mutually agreed to discontinue after three weeks. That's obviously not a helpful experience for the student at any rate, and it could have been avoided if the guy had been more self-aware about the limits of his skills.
Perhaps you feel that you've covered your back (and perhaps your conscience) by offering it gratis and hence on an "at your own risk" basis? However I have to wonder why you're doing that anyway - is it for the CV? Private tuition ought to be charged, even if at a nominal rate; when so many tutors in your area are charging significant rates and getting clients, for you to offer it for free sounds a bit too good to be true, and if I were a prospective client (or their parent) I'd actually be a bit suspicious....
Well aren't you just the handsome chad
What exact form does the "hitting on" take? What do they do or say that convinces you that that's what they're doing?
If you're the first to raise the subject explicitly then I admire your guts
You have to be sooo sure that they weren't just play-acting, before you come out with a caution like that. Can't imagine how cringey it would be if you ever misread them and then warned them off something they were never thinking of?
That sounds totally realistic, that's just the way "women scorned" behave. But it's infinitely better than being "fired", or worse, by the parents for making unwanted advances on their precious poppet!
Either you've only just started tutoring or you've had extraordinarily back luck in terms of the fanciability of the girls you've tutored. By the way, you've only mentioned girls - do you never tutor boys? Is this your deliberate policy? Hmmm...
I'm pretty amazed that any young person in this day and age doesn't know this and needs to google for it, and doubly so that anyone could venture into tuition without arming themselves with facts as relevant as this....
The age gap is really nothing. And as you say you're prepared to wait for her, I guess we're not going into the ethics of premarital sex and all that (dozens of threads on that sort of thing already).
The precise question to ask is whether it would be wise for you two (assuming, as you've claimed, that you both like each other) to get involved romantically while tuition is ongoing. And frankly, I think the question only arises when the feeling is mutual, because if it's unrequited by either side, the tuition is likely to come to a rapid end. My personal opinion is that since you've started to help her at her maths, your priority (and hers) should be to carry this on without compromise until the exams she's working towards (Year 12 in your case, which I think will have finished by the time of my writing). Then what you do afterwards is free from worrying about failing to deliver value for money - or rather in your case, honouring your initial word to get her up to speed on the subject matter.