What could it be compressor or relay?

If the fan only works at certain speeds its usually the resistor located on the fan motor. Cheap and usually very easy to change. Also, AC will not work on the defrost setting. It uses the defrost vents to recirculate the cold air in the car. Its easier to cool the air in the cabin of the car instead of the hot air outside, so the system is designed to only work on the recirculate setting and to use that setting it needs to use the defrost vents to suck in all the cold air coming from the other vents.