1) I'm fairly certain your Civic's crank pulley has separate belts for each accessory, so cutting the A/C belt would be fine.
2) A tune-up of that sort is always a good idea on an old and probably neglected car.
My #1 technique for raising my economy has been to slow down. I try to never drive about 55mph, as this is what happens to economy as speed goes up:
(stolen from a fellow member here on Ecomodder)
