Thank you so much for this great feedback !
Yes, it's true that after that message, there are no more new mechanics, except for the last level where the platforms are smaller ( I would have liked to have more time to create additional levels, but it wasn't possible in 5 days )...
Once the power-ups have been learned, they are available in all the following levels, but they are not necessarily required to complete the levels ( although they make it easier ).
Regarding wall jumping without the green power-up, I intentionally left one frame that allows you to do it without the power-up ( and then it's blocked if you don't have the green power ) to let speedrunners go faster if they manage a frame-perfect jump.
Well done for finding that Easter egg !
As for the jumps, they reset as soon as you touch a platform, and you can use them at any time. So, yes, it's possible to drop and then jump farther ( by using this mechanism, you can also reach otherwise inaccessible areas and go faster ).
You can change controls in the "Settings > Controls" menu but only on keyboard for now...