Is the method of exchanging currencies in forums—where an amount is reserved and sent by mail, then receipt is confirmed—considered a valid session for [mutual] possession (majlis al-taqabud), or is it an usurious transaction, and what is the ruling on dealing with the account opened with the money resulting from it and using the application purchased with it?

Exchanging currencies is called sarf (currency exchange). If the currencies are the same, the conditions for sarf are equality and immediate possession (taqabud) in the same session. If the currencies are different, the condition is only immediate possession in the same session. Paper currencies have the same rulings as gold and silver in terms of usury (riba) and zakat (definition). When exchanging dinars for dollars, actual or constructive possession must occur within the same session. Actual possession is the exchange of the two currencies hand-to-hand, while constructive possession is achieved by depositing the funds into an account or receiving a bank check. The scenario described in the question does not constitute valid qabd (possession) according to Islamic law, because the delivery of the two currencies takes place at different times. If this deferred exchange has occurred, repentance to Allah is obligatory. If the money is still available, it must be returned to its owner. However, if it has been spent, returning it is not obligatory, and it is permissible to benefit from what was purchased with it.