Without bothering to read what's been posted in this thread so far:
Time rankings on elitescores:
http://www.elitescores.com/rank_wr.php?gid=8
TAS forum topic:
http://tasvideos.org/forum/viewtopic.php?t=2181
There are videos posted in the forum topic, but I haven't checked them out. Ideally, you should aim to improve the times posted on elitescores or the times the players reach in the posted videos.
1. You can use TASinput which will hold whichever key you 'checked' until you 'uncheck' it.
I don't know any answers to your other questions, sadly.
You should use one of the Dolphin versions posted
here (3.0-381-dirty (TASInput branch))
This version is said to be completely desync-proof.
Also, you should use these settings in the config menu:
---GENERAL TAB---
Enable Dual Core (OFF)
Enable Idle Skipping (OFF)
-> JIT Recompiler (recommended)
Lock threads to cores (OFF)
DSP LLE on thread (OFF)
---AUDIO TAB---
-> DSP LLE recompiler
Enable DTK Music (ON)
Enable Audio throttle (OFF)
If you use these audio settings, you need two files named "dsp_coef.bin" and "dsp_rom.bin" that don't come with dolphin for copyright reasons. And for the same reason I don't think it's safe to post them here, sorry.