I would say yes to questions 1 & 2. There is definitely no hard requirement to complete a formal on-campus UX qualification. I suspect you’ll find that the majority of people here didn’t.
Regarding 3, I think that talking to people that have already done the courses is a good idea. They can be very differently balanced with some pitched at self-directed learners and others with a lot of mentorship and hand-holding.
@jdebari would be a really helpful person to hear from here. She mentors for several programs.
A portfolio is a big part of the process although I do know of successful UXers that have survived without one (e.g. @AshleaMcKay). They don’t have to cost money though. In fact, most don’t.