Are the remaining installments on the disputed car — given that it is registered in the name of the deceased father but designated for the son — an obligation of the father or the son? And do defects discovered later in the car reduce the amount that must be paid?

Since the deceased father bought the car for his son, and the son is responsible for paying its installments, the son is the one obligated to pay the debt. The father's liability is not engaged unless he was a guarantor for his son in the payment. The death of the guarantor does not invalidate the guarantee, so the debt is paid from his estate, and then the heirs can claim it back from the son. As for the discovered car defects, if they were flaws that diminish the price and existed before the purchase, the son has the right to annul the sale and reclaim the price, or to receive compensation for the defect (arsh al-'ayb). However, after three years have passed since the sale, with knowledge of the defects, and without demanding compensation for them, and with continued use of the car, this indicates satisfaction with the purchased item and forfeits the right of option.