Is it permissible to purchase an apartment through a bank for the purpose of renting it out and providing additional income for a divorced woman and her daughter?

There is no objection to purchasing an apartment through a bank if the transaction adheres to Islamic Sharia (definition) regulations, among which are: that the bank must own the apartment before selling it to the client, and that it does not stipulate a penalty for late payment of installments. If any of these conditions are violated, then it is an interest-based transaction which is impermissible. And if the bank lends you the price of the apartment with interest, then this is precisely the forbidden usury (riba), and it is not permissible to proceed with it except out of necessity.