So there is really just a couple of things.
First, as I said, I cannot reach this lever in level 3, not level 1:
Second, I died almost 50 times just trying to pass through these two spikes on the top of each other in level two. And the fact that the player always spawns in this place doesn't help:
Maybe it's not a problem with the jumping mechanics itself, but with how the obstacles are positioned. Other than that, everything works fine and I've really enjoyed playing the game!