Rolled oats are to be soaked overnight (actually, I think the recommendation is 8 hours). They will be more soggy than unsoaked oats, yes. If you don't like mushy stuff, you could use steel cut oats instead.
I don't think there would be any difference between the mason jar and the bowl.
Store kefir would be fine for soaking. I drain whey off of yogurt (often store bought).
Another way you can ferment grains is by adding miso to cooked grains (or legumes - I LOVE that) and letting them sit for about 8 hours. That is the way I do rolled oats, rather than soaking.