Is it considered usury for a person to contract with another to build a house in installments, on condition that the builder purchases the building materials after the agreement and before starting construction, knowing that he does not own them at the time of the contract?

This contract between the questioner's father and the individual is not an interest-based loan, nor is it a sale of what the individual does not own. Rather, it is a manufacturing contract (Istisna'a), which differs from sales and rentals, but resembles them in some aspects. It resembles rentals in that work is part of the contracted object, and it resembles sales in that the manufacturer provides the materials in exchange for compensation.