What were the conditions to be fulfilled for a free man in the (LATE) Medieval ages, to be accepted by a university as a student?
The minimal requirement to study the liberal arts seems to have been sufficient financial means to support yourself and pay the fees, which usually implied that you were of good (or at least moneyed) family background. You also needed the ability to converse, read and write in Latin, and a basic understanding of Christian doctrine. That seems to have been all the mandatory requirements, although more education would be useful.
The interview process was essentially "turn up and find someone who's willing to take you on as a pupil." The early universities were essentially guilds of scholars who collected fees from pupils to make their living. Travelling was expensive, dangerous and slow; making a special journey to be interviewed would not be plausible, unless you lived quite close to the university.