Is the young man's repayment of the installments on a house his father built with an interest-based loan considered aiding in usury, and how can he extricate himself from this situation without angering his father, who refuses [to acknowledge this]?

First: Refraining from an usurious loan is correct and is not considered disobedience to your parents, for there is no obedience to a creature in disobedience to the Creator.

Second: Your father must repent from usury while continuing to make payments. There is no harm in benefiting from the house or in children residing in it. The father owns the right to sell it, rent it, or gift it.

Third: Whoever takes an usurious loan falls into the unlawful, but he owns the money and is permitted to benefit from it, as the Permanent Committee has ruled: "The house is not to be demolished; rather, it is to be benefited from by dwelling or otherwise. Repentance, seeking forgiveness, and regret are obligatory."

It is obligatory to advise the father gently and explain the seriousness of being complacent with Allah's limits.