Is giving money to a friend who was short of transport fare, in exchange for taking a smaller amount of money that he had, considered usury (riba)? If it is usury, how can one be absolve oneself from it, and is only the increase considered usury, or the entire amount?

This transaction is a loan, not a currency exchange, and it does not involve usury (riba). Intention is influential in transactions, and a loan is a contract of aid and benevolence. It is permissible to return a portion of the loan in the same session, provided no term has been set for it, as a loan is due immediately unless a term is stipulated. There is no problem in taking a portion of the amount and leaving a portion, and if there is no intention to take the remainder, then this is an act of benevolence.