Welcome to TASVideos! Great to see you're working on a GameCube game (so am I!). I'll answer your questions:
1. If a key is pressed every frame for three frames, it would be the equivalent of holding that key for three frames. There isn't a way to alternate pressing and releasing a key any faster way, and the game will think you're holding the key down instead of pressing it two or three times, meaning on-off-on is the fastest pattern that the game will accept.
2. If you're trying to make an optimal TAS, I
strongly advise you to use frame advance. If the run isn't as fast as you can make it, it will probably be rejected. But if you're just slowing down Dolphin to test some strategies, then I would recommend changing graphics settings, such as increasing the resolution the game runs at.
3. I don't know why the TAS input window isn't working in that situation. As soon as the window is opened, it should be the only input being recorded (as other sources of input are disabled). When you close the window, the game should start receiving input from your controller again. Does that function work for you?
4. I don't know the answer to this one, but someone who has worked on finding memory addresses for 3D games could help you (like the Sonic Adventure 2: Battle TASers).
5. Dolphin has a built-in Action Replay that can be accessed by right-clicking the game on the game select list. I tested it a little while ago on 3.0-378 and it didn't work, but I know it worked for r7719, so maybe you could test stuff out on that revision if you have problems getting it to work.
6. Yes. Please see
this thread. In short, uncheck Enable Dual Core and Enable Idle Skipping, use LLE audio (you will need two files from a real GameCube/Wii for this) and please use the revision 3.0-378 "more-save-fixes". That revision has been out for a few months and thanks to nitsuja's save fixes,
no one has reported any desyncs in the movies it creates. The link to that revision and the "improved TAS input" revision are in the thread I linked to. If you're using any other revision, the movie file you're currently making won't sync. Usually, you will be able to hex edit a few inputs and it will sync fine.
Dolphin does not currently have any Lua support. And Wii Remote input recording is still broken, though Wii games can be TASed if played using a GameCube controller (like
Muramasa).
If you have any other questions about Dolphin or GameCube TASing, ask any of the Dolphin thread regulars (including me) here. We would be more than happy to help you.