Is borrowing from the Housing Bank in the form of a promise to sell – whereby the bank purchases the apartment, then it is registered in the borrower's name with a mortgage, and installments that include variable interest are paid – considered Haram, and what is the possible solution for someone who cannot pay in full now?

This transaction is forbidden if the bank buys the house for you and registers it in your name, then charges you installments with an interest that can increase or decrease, and the house remains mortgaged to them until you complete the installments. This is pure usury (riba). The solution is to repent and pay the remaining price to the bank, or declare your inability so that they sell the house, take their right, and return the remainder to you.