Is it permissible to pay off a debt with a different currency by transferring an amount from the debtor's money held by the creditor, and does the same ruling apply to taking wages in the same manner, and are these scenarios considered currency exchange that requires immediate possession?

It is permissible to take on debt in this manner if the capital owner grants permission. It is not a condition to deliver the debt hand-to-hand. It is also permissible to repay the debt in a different currency at its value on the day of repayment if the creditor and debtor agree to that at the time of repayment, as stated in the resolution of the Islamic Fiqh Academy and the standards of the Accounting and Auditing Organization for Islamic Financial Institutions.