Check to see if the 10 HVAC fuse in your 1998 Chevrolet Cavalier has power when the ignition switch is in the "off" position. The the fuse has power you will need to find out why. It could be a faulty ignition switch or a problem with your aftermarket remote start system causing the HVAC circuit to be powered up when the ignition is off. I would suspect that the same fault is causing the blower motor and window problems - and there may be other thing staying on that you don't know about. The orange wire coming from the ignition switch is the one that is staying "hot", checking that circuit at the ignition switch would be a good place to begin diagnosing the problem.