It's hard to set any rules for placement of "się". I would say "Muszę się uczyć!", but "Muszę uczyć się do egzaminu!" - frankly, getting a lot of immersion in Polish may be the only way to find out what is more natural. It's probably better to avoid 'się' at the end of the sentence.

Remember that 'się' can be situated quite far from its verb: "Muszę się do tego egzaminu który będziemy mieli w przyszłym tygodniu naprawdę dobrze przygotować".

Look ar page 65: https://www.docdroid.net/K5bFCXa/lessontotal.pdf.html. You should also remember that "się" like many monosyllabic words can't stand at the very end of the sentence.

Well, it would mean that you have to be a student of a university. When you're a student of Law, let's say, that means you "studiujesz prawo", but when exams are coming, "uczysz się do egzaminu".

The question is, whether "I have to be a student of a university" version would be put by a native in the same English wording or not...

I think that using "mieć" as a modal verb is best translated as "to be supposed to".

So "Mam się uczyć" = "I am supposed to learn".