What is the ruling on sending $500 to a bank account in one's home country via a friend in a third country, where the amount is handed over to the friend's father in the sender's country, with the transfer fees added to the amount or paid separately, and is this transaction considered a form of cooperation permissible by Sharia?

There is no objection to the aforementioned transaction if it is in the form of a loan, meaning your friend loans you the amount and transfers it to your account, and you repay him the amount plus the transfer fees, with no obligation for immediate repayment. However, if it is agreed that it is a currency exchange (sarf), then the amount must be handed over to your friend's agent immediately upon the arrival of the transfer to fulfill constructive possession, and the fees are paid as part of the currency exchange process.