how to seperate a clutch fan...out of the car

Okay, I think I understand. What you are calling the "backing Plate" is an electro-magnet coil that energizes the clutch assembly causing it to pull in and drive the compressor. It should be a slip fit into the clutch assembly and easily lift out by using your fingers in the inner mounting hole. There is nothing mechanically, like a bolt, holding it in there. If it won't easily lift out there may be something , like that missing woodruff key, jamming it in there.

To reassemble the clutch assembly on a compressor those three little screws hold the magnet coil assembly to the face of the compressor and the compressor shaft is centered in the hole in the coil. When the clutch is installed back on the compressor shaft the clutch should freely rotate around the magnet coil.