Can you run the a/c in a vehicle, selecting the air direction as defroster (up on the dash) without damaging the a/c unit or parts thereof? Would you damage the evaporator?

It's counter-intuitive, but yes you can have both on at the same time, without damaging anything. You would only know this if someone told you or you read the Owner's Manual. It's how you use the defroster and keep the car from fogging up in the winter, by dehumidifying the air. This is very important to know about small cars, which are prone to fogging up. Glad you asked.