I power level out the first several levels of fishing by building a tiny shack right on the edge of the shore with a fire to keep rested and resting buffs up for the xp bonus, then i just cast and reel, cast and reel. You get fishing experience from reeling in regardless of whether or not you have a fish on the line. Seems to be slower than if you do, but at least it's still quick for the first 20ish levels to get you to a point where your stamina doesnt drain as fast.

It is confirmed that stam drain increases as you go up the biomes in fish, and yes, you are correct, quality of the fish also impacts stam drain. It's designed to make you level up fishing in meadows, then move to black forest when you skill up a bit, and so on. You can always use the Eikthyr ability if you really need to catch higher tier fish.

Cooked fish meat is an ingredient for the fish wraps recipe once you get barley flour.