AC compressor is just for AC. If you turn the AC you should hear the compressor engage. If not it could be a bunch things, from low pressure, bad switches, bad relays, etc. AC system is a bit tougher to work on than heat. First step would be getting some AC manifold gauges or have someone look at it.
You get heat from your engine pumping coolant through the heater core. Under the hood you should see a place where 2 coolant hoses go through the firewall. Let the engine warm up and these hoses should feel warm. If not, something is messed up with the coolant flow because the heater core isn't getting hot water. If those hoses are warm, then that usually means the blend door is stuck for some reason, which blocks the heat from blowing into the cabin. Blend door could just be broken or your dash switches aren't working or connected right.