Is it permissible, Islamically, to take out an interest-based loan due to dire necessity? And does this fall under the principle of "necessities permit the forbidden"? And is it possible to purchase an apartment in installments with bank interest due to the lack of an alternative? And is it considered usury to mortgage and rent a house at the same time for dwelling?

If the intention behind paying the amount is a loan that brings benefit to the lender, with a symbolic rent much lower than the market rent, then this is usury (riba). However, if the payment of the amount is a pledge (rahn) to guarantee the landlord's rights in exchange for renting the house at a normal rent, then it is not usury, but this contract of pledge is invalid due to the absence of its conditions.