will air in coolant make a car rev up and down and then cut off

 

It can cause it to rev up and down, Yes.
I suppose air in the cooling system would throw the idle speed off along with the ignition timing. Which would make it "cut off".
Not 100% on this tho hopefully someone can chime in.

IMO, why not just bleed the air from the cooling system and give it a try? Takes like 10 min MAX, and is very simple to do.

 

i tried bleeding it by filling it up with coolant and letting it run and then bleeding it but after a while it goes to real low rpm and then dies also my fan doesnt cut on but i tested it and it works

 

Run for a while with the heater set to full hot. Stop and let the engine cool off completely then take the radiator cap off. The radiator should be full to the top (car must be on a level surface). If that is OK you can conclude the system is free of air.

Don't worry about exactly when the fan cuts on (if ever) unless the engine is overheating.

 

i dont know what year you have but you might have a bleeder valve at the end of the top radiator hose one the block side.. if so (while cold) crack that valve open.. then start to fill the system with your 50/50 mix.. when it is full you should see a steady stream of water coming out of there no air bubbles.. when it comes out steady close the bleeder valve and put the cap on.. run the car through 2 or 3 fan cycles shut off the engine and carefully take off the radiator cap and top off the system.. the safest way for me is to pull the overflow cap all the way out so the pressure has somewhere to go.. the with a rag slowly take off the cap.. that should do it for you.. if you dont have a bleeder valve.. fill the system and run the car with the radiator cap off until it stops bubbling then top off the system..

 

I know the original poster probably is no longer active, but i thought I would give it a shot. Im having the same exact problem, tried bleeding the coolant, but it still happens. did you ever resolve this, and if so how?