How to remove ac compressor

no
disconnect the power wire to the ac compressor clutch
that will isolate the compressor if it has seized bit still allow the pulley to turn
if it will still not turn , have the pulley removed and a new bearing fitted

Buy a compressor bypass pulley and install it in place of the compressor

If the pulley on the compressor will not turn freely, then yes if a bypass pulley exists you would need to use it in place of the compressor.
If the compressor pulley turns but the compressor is locked up, just unplug the compressor clutch.

There should be four mounting bolts, and the fittings for the hoses on the back.

If by heat you mean defrost, it could be a seized AC compressor or compressor clutch, since the AC compressor is also engaged when in defrost mode to remove moisture from the air.

Try turning the flat, round plate on the front of the AC compressor by hand (WITH THE ENGINE OFF!!) If turns with only a little resistance, the compressor is most likely NOT your problem. If it not turnable by hand, then your compressor is seized up will most likely need replaced.

If the compressor itself has failed, you can unplug the clutch and leave the belts as they are. If it is the pulley bearing that failed, replace it, it does not cost all that much.

the bearings are seized need to replace ac compressor

If the bearing for the belt pulley on the compressor seizes, the engine can quit and even appear to be seized as well. Remove the a/c belt and try to start the engine.

tension chk aways between ALT and CP (harmonic balancer) and yes the idler (tensioner) is below the AC compressor. Recommend you replace it if seized.

Go to the parts store tell them the issue and ask if there is a shorter drive belt that will allow you to bypass the AC compressor pulley