Is it permissible for a student residing in university housing for studies for a period of five years, whose family's city is 360 km away and whom he visits every 3 weeks, to shorten and combine prayers?

It is not permissible to shorten or combine prayers while residing in a city, because the person is a resident there and not a traveler. This is the preponderant opinion among scholars. If a person visits their family, they may shorten and combine prayers on the way. Once they arrive, they should pray in full, because they have reached their homeland.