I don't use Dolphin, so I can't answer most of your questions, but:
1. The game can't tell the difference between holding down a key for two frames, and pressing it for a frame, releasing and repressing it between frames, and pressing it again, because it only reads input once per frame. So if you're trying to press as fast as possible in realtime, you're limited to pressing it once every other frame.
If you're trying to press it as fast as possible in gametime, it might be possible to pause the game, release it and repress it, then unpause the game again, as the game would have time to read the release then. (Either the release or repress might need to be timed on the same frame, or the frame before or after, as the pause or unpause, depending on the game; you can experiment. Also, this trick doesn't work in every game) This is obviously slower in realtime, so it's limited to a few tricks, like increasing the maximum speed of a BLJ in Super Mario 64, where presses on successive frames are really needed.
4. Look for x, y, and z for position, pretty much every game engine I know stores them like that. You might want to try both ints and floats, and 16, 32, and 64 bit, until you find out the values. (I'd say floats are slightly more likely on modern consoles, like the ones Dolphin emulates, but it's far from certain.) Direction is more complicated; most likely, you'll have an x,y,z value for velocity, and some other value for facing, but there are a lot of possibilities.
5. Being able to use cheat codes is useful for testing, but the emulator should be able to emulate an Action Replay for you (I don't know how it's done specifically in Dolphin), so you don't need the actual hardware to do so. The main information you get out of this is whether a memory address is correct; you can lock a memory address to a given value with a cheat code and see how the game reacts to discover what the memory address does in the game. If you're trying to do a testrun of part of the game it's hard to get to (unlikely to be a problem with Super Monkey Ball), it's sometimes also helpful to use cheat codes for actual cheating, although obviously you can't do this for the final run.
6. Dolphin used to have a lot of sync problems, but many have been fixed by now. You might want to ask in the forum about Dolphin here about how much progress they've made with fixing sync problems. Make sure you use a recent version of the emulator (preferably, the most recent one that's known to work; it's probably hosted on this site), and if you want to guard against potential desync issues, keep frequent backups of your TAS (as well as replaying it from the start every now and then to ensure it still syncs).
