What is the ruling on giving a credit card to someone to make online purchases with it in dollars, then they return the equivalent amount in Egyptian pounds, and the cardholder repays the full amount to the bank, while taking a fee from the purchaser in return for the profit gained from the purchase operation?

Your enabling someone else to use your bank card to pay for their purchases, and then they return to you the amount they used from the card's balance, falls under the ruling of a loan. It is not permissible for a lender to derive benefit for himself from his loan, as the rule is that "every loan that draws a benefit for the lender is usury (riba)." It is also impermissible to combine a loan with any contract of compensatory exchanges.