Are real estate loans from banks with an interest rate of 1%, 2%, 3%, or 4% permissible, considering that this percentage might be considered a processing fee for the file, especially since it is part of the total housing cost (part borne by the beneficiary, part by the state, and the remainder by the bank)?

A loan that involves interest benefiting the lender is usury (riba), whether the interest is small or large, and whether it is paid by the borrower or the state. As for administrative fees that are not tied to the loan amount or its duration, they are not considered usurious interest, provided that the deducted amount genuinely equals the service rendered; otherwise, it would be prohibited usury.