EDIT: I posted my message without noticing another one appeared minutes before lol
I also have the same questions Dimon already mentioned before, but I can answer them because I'm familiar with this game:
1. The game seems the developers "forgot" testing it before releasing in Japan: it lags too much that while destroying an enemy may remove some lag frames, the way how the game lags is inconsistent - if you manage to remove one lag frame, you must test the rest of the stage because the system is easily prone to desync.
2. It's possible indeed, with good timing.
3. The invicibility item seems to increase lag, but it's actually possible to kill any enemy by simply doing a small brake (pressing the opposite direction) for 1 or 2 frames even during diagonal sequences. In short, you can actually save more seconds ignoring that item.
4. Unlike most games, not jumping off ledges may be faster because there a hidden mechanic that requires holding the opposite direction and on the next frame hold left+right buttons (2 frames before you start falling): Marty will keep the max speed and not lose the speed when he lands.
5. I don't remember well how the walls behave but in the 9:22 case Marty kept some speed at least.
Sorry to disappoint the author, but I have an unfinished project of this game whose includes more tricks I've found between 2016 to 2019 in addition to unexpected several timesaves:
https://tasvideos.org/UserFiles/Info/638991462937706011
This is a very tough game to TAS: 80% of the time you need to avoid lag frames when possible. Blame the developers for not refining the gameplay to the fullest potential.
The second boss can be manipulated by finishing 2-1 earlier or later. I'm not sure if pausing the game during the actual battle allows benefit too. But the third boss, while looks tough to defeat, it's actually possible to hit him more times without waiting through careful control.
I can't decide about the rest of the game because I need to study my abandoned project again :\
Last time I touched this game was during 4-2 that requires further testing because this stage sucks.