Is the increase in the price of a house—which was purchased through deferred payment, with a portion of its price already paid—permissible if stipulated by the seller, whether at the initial agreement in the event of defaulting on the payment due date, or after the initial agreement session and before the expiration of the term, or after the expiration of the specified term between them?

A sale is a binding contract, obliging the seller to deliver the sold item and the buyer to pay the price. The debtor's inability to pay does not permit the seller to increase the price on him. Such an increase is forbidden, even if done with the buyer's consent, because Allah Almighty says: "And if there is one in [financial] difficulty, then [give him] time until affordability. But if you remit [it as charity], it is better for you, if you only knew." And a procrastinator's honor and punishment become permissible. The Fiqh Academy has ruled that any increase on a debt when the debtor delays payment is forbidden, and that a wealthy debtor's procrastination is forbidden, while also stating that it is impermissible to stipulate compensation for delayed performance. Therefore, what the seller took in excess from your father is unlawful and must be returned.