Is it permissible to borrow money that originated from a bank loan, on the condition that the loan amount be repaid without interest, but with a promise to give a gift, and is this gift considered a compensation for the loan?

It is permissible for your friend to borrow money, but it is not permissible to promise a gift in return, for a loan is a contract of donation and should not be exchanged for a benefit. Every loan that draws a benefit is usury (riba). It is obligatory to advise anyone dealing with usury, urge them to return what they took from the bank, and remind them of the severe warning against usury.