Is it permissible to purchase goods with foreign currency using one's personal credit card, provided that the buyer repays the same amount in foreign currency but at the selling price (the higher rate) of the local currency?

This transaction is impermissible because the agreement for a person to borrow an amount from you in dollars, on the condition that he repays it at its value in local currency, is considered a deferred exchange between two usurious parties, and this is usury (riba). The fundamental principle is that a loan must be repaid in the same currency that was owed by the borrower. Modern banknotes have the same rulings as gold and silver, and when exchanging between them, it is a condition that it be hand-to-hand.