Is it permissible to move to live near the university to facilitate eating and studying, and to pray at home, even though the current residence is close to the mosque?

There is no objection to moving to accommodation near the college, and you may pray in congregation with your colleagues if possible. Otherwise, it is not obligatory for you due to the absence of a nearby place where congregational prayer is established. One who does not hear the call to prayer with a moderate voice or finds it difficult to go a long distance due to illness or the like is excused. Try to attain khushu' (devotion) in your prayer and ponder over what you recite.