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Question. Does the car have spark at the spark plugs? What is the fuel pressure reading?
Without seeing the vehicle it is difficult to estimate. But going off of your description it does sound fair. Just make sure he also does an alignment afterwards.
The INFL REST light is for your air bag system, so I doubt this is causing your stalling condition. It sounds like you have attempted to fix many things first. We would need to get the vehicle in to run some tests to see what is causing the problem. It could be anywhere from a vacuum leak, to a bad sensor, or possibly a bad fuel pump. There are too many things that could cause this to know what the problem is without proper diagnostics first. Let me know if we can help.
I would have the system tested to insure it is full. A system that is low on refrigerant will not put out cold air at all vents.