(1) What is the ruling of staying in that house, for which his father would be paying interest for 10 years?
(2) If he convinces his father to clear the entire amount to the bank immediately and his father repents to Allah, would staying in that house be a concern in any way?
بسم الله الرحمن الرحيم
(1) It is severe sin to take interest based loan. It is haram to pay interest. Your cousin’s father should pay it as soon as possible and save himself from haram act. But there is no harm in the amount which your father has received from the bank as loan. Hence there is no harm in the house bought with interest money.
(2) The best method is to convince his father for paying the money immediately so that he could save himself from the evil of interest and haram act. He should do taubah and istighfar for the same, then it shall be lawful to stay in the house without any hesitation.
Allah knows Best!
Darul Uloom Deoband