AC DISCHARGES THE GAS

Possible, but before I did that I would try to make sure the signal wire from tank to gage is "intact" not shorted to frame for some reason.

THE CRANK SENSOR IS LOCATED ON THE ENGINE BLOCK NEAR TRANSMISION BUT CALL YOUR DEALER THIS TRUCK HAVE A RECALL FOR THE SENSOR

I had the similar problem with my 02 santa fe. Someone said it is the crankshaft sensor. How is yours now?

Answer: NO... you must/need to vaccum the system to remove moisture from the system before you recharge it. Otherwise, you could damage the AC system

you have moisture in the system this causes your expancion valve to freeze up an stop working, thats why it works for sort time and when it de-freezes stars working again. you need to do a EVAC & RECHARGE with a good AC service equipment, specially attention to pull vacumm por at least 20minutes so you get all moisture out of the system.
Good luck

it was running then you removed the gas cap to fill ( extremely dangerous practice with car running)
that indicates that there is a problem with the EVAP system.
run the fault codes ( what the dealers should have done first ) and check for the EVAP codes , purge vent or solenoid problems

I would first make sure you didnt over fill the system, you may have to exvacuate the system and then recharge it, then watch to make sure the cooling fan is colling condensor, if fan is not working that may be the problem,next if fan is working i would check for power at clutch, this will tell you if the clutch is bad or if its loosing power to clutch,you should have gauge to watch the hi and low side preasure readings.

check to see if you have power at the AC AND HEAT blower motor.if yes your blower motor is defective.if you have no power to blower motor look at fuse- blower relay-resistor or bad control switch.

If your Santa Fe has a V6 engine 2.7L , it sounds like you have an ignition break down happening. You will need to renew all the ignition wires and check the two coils also for arcing .

haynes has one id try bleeding the brakes or replace them an bleed