Is it permissible for a father to grant his eldest son a house without the rest of his siblings, on condition that the son pays the father a monthly rent for the house for a specified period, then repays him the full sale price, and is paying rent considered usury (riba)?

This transaction is considered a loan with interest, which is forbidden usury (riba) and impermissible to engage in. There is a consensus that "if a loan (salaf) is conditioned upon a tenth of the loan as a gift, or an increase, and one loans it on that basis, then taking the increase is usury."

It is obligatory to be just among children in giving gifts and loans, and it is not permissible to single out one of them with it while excluding their needy siblings.