Is it permissible for a student who woke up in a state of major ritual impurity (junub) and has no access to tayammum to perform ablution (wudu') and pray with it, given that the time for ghusl (ritual bath) is scheduled by the university for a later time, and is he required to repeat the prayers he performed before that?

We have previously explained the invalidity of a ritually impure person's prayer with ablution without a full ritual bath (ghusl), and the obligation to repeat the prayers he performed. Similarly, dry ablution (tayammum) is not valid except after seeking water. A ritually impure person must perform ghusl with water. If he is prevented from doing so at the university, he should perform ghusl in one of the mosques if possible, as ghusl from ritual impurity is obligatory and is only waived due to inability. If you are unable to perform ghusl due to the lack of water or a suitable place, then tayammum is permissible for you.