Do I have to use a mason jar to ferment veggies? Or would any jar do? In case of the latter, does it have to be air sealed?
Any water-tight container can be used for lactic fermentation. The main thing you want is a way to keep the vegetables submerged in the brine, usually a wide weight placed over the vegetables, so a jar which narrows a lot at the top will be trickier to work with. (Using a plastic container may give a bad flavor.)
You should not seal a container being used for fermentation. Gas pressure will build up, and possibly make the jar explode.