Is the process carried out by the inquirer, and the resulting exchange rate differences, considered permissible or impermissible (halal or haram)?

The ruling on purchasing currencies with a credit card depends on the terms of the card and the bank. If the bank is Islamic and the card is free from Sharia prohibitions (such as usurious interest upon delayed payment), then the default ruling is the permissibility of selling currencies, while observing the Sharia regulations concerning currency exchange, such as the condition of immediate mutual possession when exchanging one currency for another of a different type.