Wow, I didn't expect that comprehensive of a reply. Thanks Kirua, you're the best!

I can do the fire kill on Wendy (badly), so it sounds like I should make it a priority to learn the world 1 one, and not worry about the others for now. I still have a bunch of macro-level stuff I should learn first (2-4?, the new 3-2, the new 4-4, 7-F2, consistent 8-1, etc.).

It makes me happy to hear that there's still stuff to explore in this game. I've been kind of worried that I walked in on a pretty much solved game.

Thanks, that was really helpful! I've got a few follow up questions, though, if you don't mind:

1. How many patterns do the koopa kids have? Is it way too many to learn all of them and react to which one you see?
2. You say it's easy to enter airship pipes asap--is there a way to buffer this or something? The way I currently do it is by walking at the front of the screen and hitting down when it looks like I can go in, but I feel like I'm by no means frame-perfect at that.
3. Is it really possible to consistently hit the same 8 frame window going into a fight? It seems like (non-buffered) overworld inputs are going to vary by a few frames each, and mashing for the toad dialog box should vary by that much too, even if you can buffer the pipe input. If your average pipe enter time isn't right in the center of the 8 frame window, you could mess up by just a couple of frames and get the wrong pattern.
4. What would you suggest doing to learn the fire kills? Should I just study some runs and try out what I see?

I'm having trouble practicing things with RNG involved (e.g. boss fights, hammer bros) because with save states, I seem to get the same pattern every time. Does anybody have a good way to work around this?

Also, is it bad to start runs from a savestate on the title screen? Does that save your RNG seed in any non-kosher way?

Makes sense, thanks. Trying this out, it feels a bit unnatural to buffer 1 input and then go back to inputting normally, but I'm sure I'll get used to it.

Up until now I've been moving in the overworld by tapping the direction I want to go only after mario is free to move. Recently I saw that you can skip hammer bros on screen transitions by holding down a direction during the transition. This made me wonder if you could move more perfectly by pre-selecting your movement direction before you're actually able to move. When I tested this out it seemed like it worked perfectly sometimes, but sometimes you're stuck in place for awhile before you can move. I couldn't find a pattern to when it works and when it doesn't. Does anybody know how this works?