No payments in foreign cash are allowed in Belarus (except for payments for gas at filling stations). You may pay with your bank cards in most of the bars and stores. You can also pay with your bank card for the taxi 135 (warn the dispatcher before requesting a car).
Don’t change your cash privately: the fine is $1500, foreign cash will be confiscated. Change your cash in exchange offices, only (those at the central train station work day and night).
An average cost of a taxi ride is 14 BYN ($7), a drive to the airport will cost you $30. You should drive official taxis and ask for a receipt, so that you don’t overpay.