Sorry to hear of the lies you were told. I was told my first horse was 8yo when I bought him, only to find when I got the dentist for him that he was closer to 16yo! I would be very cautious of purchasing a horse without a vet check these days.
Speaking of dental work, a horse generally needs their teeth seen to once every year or 2 in middle age. However, if they wear a bit or they eat grain or such, it may be needed more often.
Re picking her feet up, yes, of course it's a behavioural issue, but as with everything, of course there are always good reasons(for the horse, anyway) for any 'naughtiness', whether it's physical or not. I don't think there's likely to be a physical problem with picking her feet up now, so you should be able to start working gradually & providing lots of well timed reinforcement, so that she's able to be trimmed asap.
I don't understand why gravel would be OK if tar isn't. If it's because the toes/breakover are too long, so that the leverage on them is too strong on hard ground, I would advise staying off the gravel too, until you can get her trimmed properly. If it's just that her feet are generally weak, a paved road should be easier for her than loose stones. Paved roads are generally easier to begin with for a transitioning horse than gravel roads or tracks, because they're smooth.