Is it permissible to establish Friday Prayer in a small prayer area designated for university students, given the existence of large mosques a fifteen-minute drive away, and for the purpose of alleviating pressure on the major mosques?

It is not permissible to have multiple Friday prayers in one town unless there is a need, such as the mosque being too small for the worshippers. If the condition of the mosque is as you described, that it is too small for the worshippers, then this is a need that permits establishing the Friday prayer in another location. However, residence (istiṭān) is a condition for the Friday prayer. If you are students residing for study and intend to return to your home countries, then you are not residents (mustawṭinūn) and it is not valid for you to establish the Friday prayer by yourselves. Rather, you must establish it with the residents. So, if there are residents with you in the university accommodation who pray Jumu'ah with you, and the mosque is too small for the worshippers, then there is no harm in establishing another Jumu'ah prayer. But if there are no residents with you, or the mosque is not too small for the worshippers, then it is not permissible for you to establish the Friday prayer. Rather, you must seek to pray it in the mosque.