We've covered some of the history of the medieval university system here before, and while you're waiting for fresh answers to your question you might like to review some of these resources.

First, there's a section of the FAQ devoted to Formal Education and Universities. And u/sunagainstgold has written an excellent and detailed response to a query about the way in which study at medieval European universities worked in the late 14th century.

I looked at the medieval examination system at Cambridge (which was based around oral disputations, rather than requiring written papers, and hence pretty much excluded the possibility of plagiarism), and this attracted a follow up on Oxford on the same thread from u/Naugrith. My response contained a fairly detailed description of the Cambridge disputation process, which was almost certainly pretty much exactly the same as the one in use at Oxford. These two answers were based on the official histories of Cambridge and Oxford, respectively.

There was also a long thread several years ago on gaining admission to, and graduating from, a medieval university, led by u/Whoosier.