Is what a bank offers considered an interest-bearing loan if it requires depositing a sum of money with it for a known period before granting the interest-free loan (qard hasan), while taking a small amount for "paperwork fees" and employee costs?

For a bank to offer interest-free loans without any increase is good. However, if it stipulates saving an amount with it before the loan transaction: If the purpose is to verify the borrower's solvency and ability to repay, then there is no harm in it. But if the purpose is for the bank to benefit from the saved amount, then this is not permissible, because it falls under the category of "lend me and I will lend you," and because the bank gained an increase from its utilization of the amount saved with it.

As for the fees the bank charges, if they are actual administrative fees, then there is no harm in taking them from the borrower, and they are like the wage of the measurer and the weigher. However, if the administrative fees are taken under the guise of fees, but they are not actual fees, then this is usury (riba), and any increase beyond actual services is forbidden.