You can't be permanently registered with more than one GP practice at a time. However, what you can do is register as a temporary resident for either 3 or 4 months at a time (can't remember which) so if I was you, I would register with a uni GP but register as a temporary resident if you need to at your old practice when you go back home since they will know you and I think they will still have access to any old records/notes that will have been made prior to you moving surgery (though not 100% sure about the latter). One tip I would give is to not register with the GP surgery directly associated with the uni as they tend to be incredibly busy but have a look and see if there are any other surgeries that cover that catchment area and register with them instead (in my experience, that took waiting times for an appointment down from 4+ weeks to days, but of course things may be different in other cities)
With regards to secondary care specialists, I suspect you would not be able to keep your old ones but I would contact them directly to ask. They may be able to liaise with specialists in your uni city to arrange transfer of care, but if not, they will tell be what the best thing to do is in terms organising follow up in the uni city.