Really awesome man, I loved it. Very tough, but people who like puzzlers like tough. I would recommend making lvl2 a little easier though as lvl1 was kind of just a joke and then 2 was a legit puzzle.
Use the levels to explain the rules. I feel like you did that pretty well, but just a little to fast/aggressive. like in lvl2 I figured out I needed to "capture" the lil crystals instead of just get them and in lvl3 i figured out using falling to change your position. But I would go even farther than that in the beginning levels and teach basic movement. like you could have pillars with "W", "A", "S", "D" on them that you need to fall on sequentially in the direction of their label (if that makes sense). And then for the next level make one similar to the first level, except add a 4-space platform next to a crystal that players have to use to orient themselves to capture the crystal instead of destroy it.
I also don't understand the name "The Cage" but maybe because thats to be revealed in later levels. "Pillar" is a cool alternative if not.
I think you have something here!