What is required in the case of exchanging two currencies online, where each party deposited an amount to the other at the same moment, then the transaction was canceled due to a glitch on the transfer website and neither party received their money? And is it permissible to repay the amount in installments due to a sending limit?

The first exchange (musarafa) between you two is void due to the absence of immediate possession (qabd). Your friend's money is a trust (amanah) with you. A new exchange can be initiated for each installment at its daily rate. This means you take possession of the equivalent amount from the money you have, and then transfer the installment to your friend's account. This is considered constructive possession (qabd hukmi), and a delay in the bank entry for customary periods is overlooked, provided that the currency is not disposed of during that period until after the effect of the bank entry.