Sorry for derailing that other thread.
I have evidence of early entrance to level 2, skipping the flower throw in my speedrun of the game
here (38 seconds in)
As far as I know it can be done on all levels on the map after the first, including level 8, where the bomb gets thrown at you.
This seems to be caused by hitting the level select button on a specific frame after exiting the previous level, but I haven't been able to get it consistent.
The Artie boss fight skip involves entering a special command once you gain control of the marker in stage 9. Up up, down, down, left, left, right, right, grab, select. Get it right, you'll hear a ping and Eryi will do 9999 damage to Artie, ending the fight about 25 seconds quicker.
Another thing I think might be quicker is, in Eryi's house, instead of running past the pan, exit to menu and go back in, you start at the marker for level 1.
By the way, I play English ver 1.02.
*Another inclusion, restarting Croco's stage as soon as you enter it skips his cutscene and makes him start throwing the spiky balls immediately, saving about a second. This may cause the UFO at the end of the game to not appear, but I'm not 100% sure on that.