Is the questioner sinful for purchasing items for his parents using his father's credit card, given that the money in it is his father's money, and the transaction does not involve usury, and the money is withdrawn directly from his father's account? And is it permissible for him to withdraw cash using the same card?

The absolute statement that credit cards are impermissible to use is incorrect. They are permissible if they are covered (prepaid) and the contract does not include forbidden conditions. Therefore, if your father's card is covered and there are no usurious conditions in its use, there is no harm in using it for purchases or cash withdrawals. However, if it is not covered or if it contains usurious conditions, then it is impermissible to use.