I'm not much of a platform player, so take comments with grain of salt.
I like the sparse and plain look, including the stickperson.
--> The instructions need a little bit of tuning. I can see how you're trying to introduce "just in time" instructions, but there's some standards you might assume (like A/D), and you might consider not forcing people to wait (for the spacebar). Especially after the first go through. You might also consider allowing arrow keys with "up" being jump.
--> I find myself sometimes being able to run on falling platforms and sometimes not. Is that intentional?
--> I find "double input" doesn't register (e.g. if I push "d" and "space" at the same time, nothing happens. I expected a forward jump.
--> In levels 1, 2, 3, I find myself sticking to walls sometimes. I don't know why. Is that the "wall merge" mechanic creeping in before introduction? Or maybe a bug?
--> Level 2 is nicely laid out - the going under and then backwards is a nice touch, especially if you are going to have players go back and forth as they go up, etc.
--> I find Level 3 really hard and gave up on it (like I said, not much of a platform player). A simple "it's probably best to keep moving" or "I'd better race through here" would help.
--> Even so, no matter how I race, I can't seem to keep up with the block falling! I also find that I am dying from falling, without really understanding why (I *seem* to fall, but when I hit the block (nto spikes) I sometimes die).
--> I would suggest at such an early level, and while introducing a new mechanic (the falling blocks) that the jump distance (and likely the timing of the falling blocks) be more generous. You want your players to feel like they're successfully learning. To me, at least, this feels punishing.
--> Another generous thing would be: ability to jump off a falling block. I can't seem to do that.