Is it permissible to take a loan from a bank to pay off outstanding debts, knowing that the father will cover the interest on the loan, and is this loan considered permissible in cases of necessity?

It is not permissible to borrow with usury to pay off debts and restore rights, even if the father bears the payment of interest, as it is not permissible to enter into a usurious contract except out of a legitimate, recognized necessity, and there is no necessity in what you have mentioned. The creditors should grant you respite until you are able to pay. One can also look for a legitimate means to obtain money, such as a Tawarruq transaction.