Air condition blows out air but not cold air..do not hear compressor at all

Assuming you hear some kind of clicking noise when you turn the AC on (the compressor clicking on):
Seals on the AC compressor likely bit the dust. GM AC compressors go out almost as frequently as tires. The good thing is that they're not horrifically difficult to replace. You can get some freon with dye in it at your local parts house. Get enough to fill it up as though it's empty (as it likely is), and see if it starts blowing cold. It should blow cold for a little while (days/weeks maybe), but when you open the hood, you'll notice some green dye around the compressor. That's where the seals have failed and why you get to be the proud new owner of a brand new compressor (don't waste your time on a used one from a salvage yard. You'll get to replace it again soon, if you do.)

You will need to know if the compressor is working when it blows hot air to proceed. It could be an electrical problem, a blend door problem, or the a/c clutch on the compressor.

Have the system charge checked, it is very likely low, if it is you have a leak.

So what does the fuse that blows, protect?

You need a wiring diagram & start to test
the components most likely to cause a high
current draw & blown fuse.

Don't keep replacing it.

You know the fan control circuit works, but the
compressor doesn't stay on. Did you monitor
the compressor as the fuse blew?

May have a module for compressor & fan
If so one side failed
The compressor clutch could be bad

Roger it sounds like the blower motor is not comming on. There is a resistor network located in the engine compartment on the passenger side mounted to the firewall, that controlls the blower motor. The connections may have corroted or the unit itself is bad. That was the first thing I had to relpace when I got my used 92 Dakota. There is also a 30 amp fuse in the fuse box under the dash board . If that is blown I would suspect the blower motor is seized up or just pulling too much power.

You have a leak & not plenty of refrigerant

Why would it try to get cold when moving at higher
rpm?

Low Refrigerant
Leaks
Air in System
Dirty Evaporator
HVAC System Doors not switching
Expansion Valve or Orfice issues
Compressor Failing
Condensor dirty & filled with leaves between it &
radiator
& More

Air Conditioner blows warm air

1. Air conditioner system is discharged. Have the system evacuated, charged and leak tested by an MVAC certified technician, utilizing approved recovery/recycling equipment. Repair as necessary.
2. Air conditioner compressor clutch not engaging. Check compressor clutch wiring, electrical connections and compressor clutch, and repair or replace as necessary.

Clicking sound you hear is the belt tensioner, due to a malfunctionig a/c compressor ,

the reed valves of the compressor are broken causing unstable pressure that makes the belt tensioner vibrate

That "thing" is part of the compressor clutch. When it’s spinning the clutch is engaged, when it stops the compressor is off. If it’s constantly cycling, you probably don’t have enough freon in the system. But remember, however the gas escaped before, it will escape again, unless you fix the leak.

To get the refrigerant in you have to have a technician purge the system first. Hope that helps.