What is the ruling on a son accepting an apartment as a gift from his father, knowing that part of the money used to build the apartment came from usurious loans? And what should he do about apartments built with mixed funds?

It is permissible to accept the apartment as a gift from your father, even if he took out an interest-based loan, because the sin of the loan is attached to the borrower's responsibility, not to the money itself. You must advise your father to abandon usury.