I played piano all through my rather demanding architecture degree, up to three or four hours a day (except in the scary bits when everything was due and I'd have to stay up four nights in a row). I was always hanging around the music library at university instead of studying. As soon as I finished my last exam, I auditioned for a music course, and now six months later, I'm working as an architect but doing music majoring in piano part-time. I can still find time to practice four hours a day, though I have basically no spare money.
I found that even though a degree like architecture is extremely time-consuming, if you don't have to work as well there will be sufficient spare time for piano practice. Think of all those obscenely giant slabs of vacation you get! Yay!
Answering your second question, I'd say learn the pieces you really want to, but at the same time give yourself a very solid musical grounding. I remember when I was younger, I would play everything the teacher told me to play, but I would always have secret pieces or compositions I'd be working on. I still kind of have the same system - I will practice all the pieces required for my exams, but I will always spend about half an hour every day playing whatever I feel like learning. I think that's important, whoever you are.