As for the Gas: I would turn the gas of when done so as to avoid costly leaks in order to save money.
As for the machine: I always let my machines run a bit after I quit welding so the cooling fan circulates cool air through the internal electrical components. I think cooling them down helps them last longer and should apply to any type of welder: engine drive, electrical transformer, or electrical inverter. Any of them generate heat doing what they do, Anyway, I have no set time that I wait as it mainly depends on how hard I feel I pushed the machine. If I ever have any doubts that I might have not given the machine enough time to cool down then I will place my hand near the intake area vents of the welding cooling fan area and then place my hand near the welding cooling fan output vents and do a rough temperature comparison by feel. If the output vent area feels warmer to me then I let the machine run some more for cool down.