A/C - Dashboard warning lights

Check the harmonic ballancer on the engine, the alternator, A/C and other accessories are all driven off the outer pully and IIRC this is attached to the crankshaft through a rubber layer which breaks down over time. My guess is the compressor is loading that down, causing it to slow and slowing the alternator as well which is causing the warning lights to go on.

If the compressor still cycles then you're probably low on refrigerant.

There's a diode on the wire going to the compressor that's supposed to suppress these inductive voltage spikes as the compressor switches on and off. It sounds like that diode may be bad. Look for a little epoxy box on the wire, grounded through one of the mounting bolts.

Also if your compressor switches on and off so frequently, it's probably low on refrigerant.