Proper woks are pretty good too but a proper wok needs a proper stove and it's unreasonable to ask anyone to get a stove like that. Woks are also pretty huge and hard to find places to store them.
It's a shame Lodge cast iron kind of sucks even if it doesn't have to. Literally all they need to do is grind down the cooking surface to a smooth finish and it'd go up in quality significantly.
You don't. At most you wipe it down with a wet cloth. If for whatever reason it needs a bit of a scrub, use hot water and some steel wool/rough sponge. If you clean it with soap, you'll have to reseason your pan.
Get yourself a chainmail scrub. The round links glide over the pan surface and shouldn't damage the layer of seasoning as much as, say, steel wool would.
If a lot more stuff is sticking to the pan than you think it should be, it may just need to be re-seasoned. "Seasoning" is kind of a gay term for baking the non-stick oil surface. You heat up an oil (it almost doesn't matter which, yes, you can use MUH SEED OILS... in fact, higher smoke points are safer/better) to the point where it's ready to combust. On a molecular level the oil starts to polymerize and adheres to the intensely jagged iron surface. It becomes hard and smooth and fills in the pits and holes. Think about how when you add butter to a hot pan with a steak, the butter actually kind of just turns dark brown and eventually a sticky residue forms... that's the polymerization.
MUH SEED OILS doesn't matter for seasoning, because the polymerization forms essentially the same thing no matter what you used.
I use bacon grease because I have shittons of it. The smoke point is around 400 degrees.
Wipe or apply a good coat of oil on the pan and throw it in the oven at the appropriate temperature for an hour, then turn it off and let it cool with the pan still inside. You can also do it on the stove briefly under intense burner heat for a quick application (I sometimes do after using it). But it can really smoke up the place.
Sponge and hot water is all you need, absolutely no chemicals. I removed egg and bacon burns a few times using that method. Learn from that mistake and use more butter, olive or coconut oil next time.
Those are the good ones for sure. cast iron pans today are shit. The vintage ones have nice smooth finish and finer crystalline structure, so they cure much better than “the lodge” brand garbage