Is it permissible to buy a house in installments through a housing program with interest, or to buy a car in installments, due to the difficulty of moving to a previously purchased house because of the long distance and the unavailability of a car?

Purchasing a house with usurious interest is not permissible except out of necessity, and there is no necessity in what you have mentioned. Buying a car in installments is a suitable solution, as long as the purchase is not through a usurious bank, because a usurious bank pays its price to the customer and charges it to him as a loan with usurious interest.