Is it permissible to remain in a house that was purchased with an interest-bearing loan from the bank, given that there is no other place to go and [the need] to continue studying?

There is no impediment to your staying with your father in this house, and you are not obligated to leave it. Your father is obliged to repent to Allah Almighty for this loan, and that is achieved only through remorse for his action and a firm resolve not to return to the like of it.