Well first of all, if your talking about a manual shift, the clutch is. more or less part of the transmission. Sounds to me like your clutch pad / disk is worn out or you burned it up. Which can happen if you slip the clutch all the time at stop lights / signs. In that case you should probably replace the clutch plate and disk replaced, and have your flywheel resurfaced.
there isn't clutch oil only transmission and engine oil
If it is an electric fan, NO. If it is a mechanical fan test it to see. If you can turn the fan by hand with the engine not running it has a clutch.
Clutch disc, pressure plate, transmission shaft,
Check the engine thermostat.
Generally if it is a thread on fan clutch, yes.Generally if it is a thread on fan clutch, yes.
If it will go into gear when the engine is off but not when the engine is running, the clutch is not disengaging. It could be the clutch, possibly warped or put in wrong, or it could be the hydraulic clutch mechanism.
Of course your clutch and/or gearbox are faulty...
The springs around the clutch plate have probably came out and locked up between the pressure plate and the clutch plate and locked them together. you need to change the clutch plate and have the pressure plate checked for damage.
The purpose of a clutch on a vehicle is to disconnect the drive of the engine from the gearbox (this would be required when the vehicle is stationary or to change gear). While the engine is running the crankshaft is continually turning, It is the crankshaft that turns the gearbox and via the gearbox the road wheels. Obviously there are times when the engine is running but drive is not required, The clutch is the mechanism by which this is achieved.
Why don't you take it to a mechanic before you ruin your truck by riding the clutch? The chattering could be engine knock because your engine is out of tune. When you ride the clutch, the clutch slips and puts less strain on your engine as you are burning out your clutch.
If it will shift when the engine is off, but not while it is running your clutch is not working
No, only if you reduce the speed so much that the engine can't keep running in the current gear.If you brake hard, you would clutch.