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The reason I said the EGR valve is if it is struck open during self test it would hold the EVP sensor open and the voltage from it would not be what the Computer expected and you would get the 31 code.
Also if the EGR valve was stuck open you would get a leaner exhaust and get the 41 code.
The one that worries me is the 13 code, that means the IAC valve is not working or stuck.
I would clean the EGR and the IAC valves with throttle body cleaner and make sure they are booth free and working.
This will not cost you much and may fix your problems.
As for the A/C, it doesn't blow cold. The belt turns the compressor but I get nowhere. I assumed it was out of coolant. Does the error relate to the switch inside the cabin or is there an interal switch on the compressor that's failing? I'd like the air to work thru the summer but the daily get up and go ability of the truck is far more important...I can sweat if I have to.
Is the inside part of the pully on the compressor turning or just the outside?