Yes, you can go to a local welding supply store and rent a tank.
Yes, you would just keep tacking a small hole to fill it in, then grind it down afterwords. Also, pulling the trigger is a lot quicker than the time it takes to grind, so go easy.
You could also purchase a carbon block at the welding supply store. If you can get to the back of the panel, you can put the block against the back, and it should stop you from making a bigger hole, or having a lot of weld protruding out the back of the panel.
And Yes, you would just cut out a piece of material to fit inside a larger hole, and then tack weld around it, until you've filled in all of the gaps.