What is the ruling on a bank deducting dollars from a client's account abroad and converting them to euros in their account in another country, while calculating a lower exchange rate for the client so that the difference between the market rate and the calculated rate serves as fees and profits for the bank? And is the bank considered an agent for the client in exchanging their money?

In this case, the bank is an agent and seeks profit. If it purchases Euros from another bank, it is not permissible for it to sell them to the customer at a different price. Instead, it should take a fixed amount for its agency. If it purchases Euros from itself, this is not permissible according to the majority of scholars, but it is permissible according to the Hanbalis if it is with the permission of the client.