Dogbone

Bypassing the belt protection system should not affect the function of the pressure switch, located low behind the front grill near the radiator. Nor should it affect the function of the evaporator temperature switch that cycles compressor to prevent evaporator from freezing.

The clicking you hear was most likely the clutch engaging/disengaging rapidly. Something is causing the compressor to cut in and out. This could either be a loose connection or the pressure switch simply doing it's job, indicating an undercharge or overcharge condition.

The screeching, probably drive belt slippage, could be as simple as the A/C belt needing tightening, or worse the compressor seizing up.