Is it permissible to finance the purchase and construction of land and residential units by selling a residential unit to the financier and then repurchasing it from him at a higher price after one year, knowing that the financier has money deposited in the bank with a fixed return?

The described financing method is a form of the prohibited 'inah sale (buy-back agreement). The Shariah-compliant methods for financing can be through Mudarabah (definition) (profit-sharing) or legitimate partnership, such as your friend contributing an amount and agreeing on a percentage of the project's profit. Alternatively, it can be through an Istisna' (manufacturing contract) for the apartments with the buyers, where the price or part of it can be paid in advance before construction.