What is the ruling on my transferring an amount from my friend's account to my account, and then giving him the amount in cash? Is this transaction considered an exchange (sarf) or a debt, and what is the ruling on conducting it inside the mosque?

Your friend transferring money to your account and then giving you paper currency is considered a money exchange (sarf). When the currency is the same, it is conditioned upon equality and immediate possession (qabd) in the same session, based on the Prophet's (peace be upon him) saying: "Gold for gold... like for like, equal for equal, hand to hand." Monetary currencies are subject to the rulings of gold and silver. Immediate possession is achieved by the money entering your account and you being given the cash, provided this occurs in one session, as a bank transfer is considered a constructive possession.

Money exchange (sarf) is the selling of currency for currency. Buying and selling in the mosque have been prohibited, as stated in the hadith: "The Messenger of Allah (peace be upon him) forbade buying and selling in the mosque," and his saying: "When you see someone buying or selling in the mosque, say: 'May Allah not profit your trade.'" The preponderant view is that selling in the mosque is forbidden. The exchange that took place is valid, but repentance is obligatory.