Is it permissible for my father to receive a 10% commission as a fee and profit from the total cost of demolishing and rebuilding a house, or is that considered usury (riba)?

Contracting is divided into two types: an ijarah (lease/hire) for work only, where the materials are provided by the other party, or an istisna' (manufacturing contract), where both materials and work are provided by the contractor. The scenario described in the question does not fall into either of these categories. It involves an unknown wage due to the compensation being a percentage of the costs, making it prohibited due to jahalah (uncertainty) and gharar (excessive uncertainty/risk). Furthermore, if the mentioned percentage includes compensation for a loan and for work, it is precisely riba (usury/interest). The solution is either to agree upon a known wage with the musta'jir (hirer) bearing the costs, or to agree upon a lump sum paid at the contract session under the conditions of salam (pre-payment sale).