Is it permissible for me to purchase items using my father's credit card, or to withdraw money with it before making a purchase, given that my father is aware of its use by him at a usurious bank, and is aware of his repayment of the loan on time to avoid usury? And what is the alternative if that is impermissible?

The default rule is that it is impermissible to use credit cards that impose a late fee, even with the intention of paying on time. However, it is permissible for those residing in the West to use them out of necessity and due to the unavailability of permissible alternatives, provided that the amount is paid before the end of the grace period to avoid late interest fees.

You may use your father's credit card in the West to make purchases for him, unless you know that he delays payment and incurs penalties. It is preferable to confirm with your father that he pays on time, but it is not obligatory to ask him, as most users pay on time.

You may not withdraw cash from your father's account using the credit card without his permission, because an agent may only act within the limits of his principal's authorization.