If you are using Innershield wire then you don't need to use gas, it uses the flux within it and doesn't require gas. If you're running regular welding wire then you need the gas.
A micro welding torch should be a smaller version of a full size welding torch - identical apart from size. It is most important a user thoroughly familiarises himself or herself with the correct usage and safety precautions because failure to observe the correct procedure can result in extreme danger. A flashback can have potentially serious consequences...
A person who is thoroughly conversant with the procedure and safety will know how to connect the hoses to the welding torch and to the cylinders - if it is a quality unit, it is an intuitive process due to the fuel gas fittings being left hand thread and the oxygen normal or right hand thread and the hoses are or should be different colours with blue being the norm for oxygen and red or orange for the fuel gas.
One final word - never, ever, under any circumstances use a lubricant on the threads of the oxygen bottle or associated fittings...
A great many older home mig welders were produced with a live torch, ie. the manufacturer had saved the cost of the contactor, the high current electromechanical relay that switches the welding current on or off in response to the torch trigger...
It was inevitable some manufacturers would replace the rectifiers and contactor with thyristors (SCRs) and obtain both functions from a single modification.
The trigger switch controls the wire motor and the contactor so if the wire motor is working ok it is unlikely the fault is there and if your welder has a contactor it could be stuck or a wiring fault has caused the coil to be permanently energised or if your welder uses the solid state version, either one or more of the thyristors have failed or a circuit fault has caused the supply to the gate to be permanent causing them to be permanently switched on.
It would seem the low current control side of the welder is working ok - you squeeze the trigger of the torch and the wire comes out and the gas flows and the the main contactor clunks?
I doubt running on a generator has anything to do with the problem and it was coincidence - if the generator voltage surge or spike was going to cause a problem it would be the control side, the sensitive electronics. The high current side is much more robust.
Welding current is supplied to the torch through a cable and is connected to the wire by the copper tip the welding wire is pushed through.
Don't worry about measuring the amps - measure the voltage through the circuit from mains voltage going into the big transformer, probably 20 - 40 volts AC from the transformer, being changed to DC and reaching the contactor and then leaving the contactor and being delivered to the torch when the trigger is operated.
If the big transformer is ok, the most common problem is with the torch assembly where the constant flexing in use often damages the pipe, wiring, main cable and welding wire liner - a lot is forced into that thick tube supplying the torch which is why professional welding machines tend to use the Eurotorch so a spare torch assembly can simply be plugged into the machine and the welding job completed.
The correct current, or amperage, setting primarily depends on the diameter and type of electrode selected. For example, a 1/8-inch 6010 rod runs well from 75 to 125 amps, while a 5/32-inch 7018 rod welds at currents up to 220 amps. The side of the electrode box usually indicates operating ranges. Select an amperage based on the material thickness, welding position (about 15 percent less heat for overhead work compared to a flat weld) and observation of the finished weld. Most new welding machines have a permanent label that recommends amperage settings for a variety of electrodes and material thicknesses.
https://welderreview.com/yeswelder-15ft-250a-mig-welding/
https://www.youtube.com/watch?v=_yTnfRS9B04So, for gasless MIG welding polarity (when using flux core wire), your MIG welding polarity settings should be set to direct current electrode negative (or DCEN). With DCEN, the negative terminal inside your machine is hooked up to your electrode (your MIG gun) while the positive terminal is hooked up to your ground.
https://makemoneywelding.com/how-to-set-your-mig-welding-polarity-settings/
There are four common welding processes utilized through out the work industry today. They are : (Stick Welding or SMAW) Shield Metal Arc Welding (Mig Welding or GMAW) Gas Metal Arc Welding (Tig Welding or TMAW) Tungsten Metal Arc Welding (FCAW) Flux Cored Arc Welding
There are many many welding processes, however these are the most common. The type I am going to discuss briefly today is SMAW. The most economical and cheapest way to learn if welding is for you or not is to start with stick welding. It has the least amount of variables that can go wrong for a beginner. It is not fast paced like mig or flux core, so you have time to watch the molten puddle to see what it is doing and make necessary adjustments to correct the size, shape, and contour of your weld bead. The hardest part for a beginner is to keep the electrode from sticking to the work piece. Thus is the reason it got the name of "stick welding". There are three common ways to strike an arc in SMAW. Tap Start, Scratch Start, and the last is to place the electrode upon your fingers like a pool cue, and shoot the rod like your playing pool.