Low oil switch cut engine off and on when cold

Not unusual. Check for loose bolts and gaskets.
Check oil before every use!

I believe the electric solenoid is a fuel shut off. solenoid needs energized, normally with switch 12 Volts. other then float bowls are the carbs. identical, if they are switch bowls, should work. If not you will have to add switched power to solenoid, the link below looked similar to yours.

Generac Generator Carb removal and disassembly

McCulloch Generator Model FG5700AK

the carb needs to be cleaned I think the internal jets are plugged

Make sure fuel tap is turned on. Tap the bottom of the carburettor with a wrench to make sure the float isn't stuck. Is the ignition on/off switch in the on position? make sure the oil level is ok as these usually have a low oil cutout which stops the motor when oil gets low. All that being ok give it full choke and it should start. Remove the sparkplug and check there is spark across the electrodes. (earth the thread part of plug on motor) If no spark replace the sparkplug.

You have a faulty inverter board on the unit. I would warranty the generator in this case, or have the manufacturer send you out a replacement board to swap yourself.

Check for faulty low oil sending unit or oil level low or dirty oil (some generators have a fuel cut-out solenoid at the carb ). Key switch will override the low oil safety. Easy test, remove wire from oil sending unit. If unit runs, and oil has not been changed in a while, service engine and retest.

Use a pressure gauge and make sure you have at least 10 psi, if you do then replace the oil pressure cutoff switch if this switch is bad no oil you put in it will fix the problem. If you don't then you have internal engines problems.

A lighter weight oil will only make the matter worse because its thinner and could actually cause the pressure to drop even further. If you have a low pressure problem you could try a heavier weight oil but its only going to increase it a little bit.

Typical diodes are 10 amp for these. The stator and rotor both have VERY low resistance readings. The reading typically will be below that which will register MEANINGFULLY on the digital meters.

My generator had 10 amp diodes with surge protectors across them. One of the protectors shorted and generator output was zero. Mine is a 6KW diesel silent unit.

Replaced the diodes with 70 amp ones with surge protectors that have 20 times the energy absorbtion as the originals. Unfortunately this required some lathe work to make holders for the diodes and the surge protectors to ride on the rotor.

Used the light bulb trick to remagnitize it once diodes were replaced.

A call to Elliott Small Engine solved my problem - Oil Guard. I had checked the oil and it was just a little low but seemed well within the normal range. I was told to add more, bringing it just over the Full mark. It seems that the low oil protection system is very sensitive and shuts down the engine even when the oil is withing 1/8" of the mark. I added about 2-3 oz of oil and no more problems

Have Generator McCullough FG 6000 was running fine motor still running fine than NO power output, any suggestions ?? Can you get replacement parts and repair diagram off the interent ??