I really enjoyed the concept of this game! With that said, I very nearly gave up on it, and probably would have if I didn't happen to look at the map and see how close I had gotten to the end. A combination of incredibly inconsistent collision and difficult controls made this experience very frustrating (if strangely addictive).
My main suggestion would be to always err toward giving the player an advantage when it comes to collision (for example, make their hitbox slightly smaller than the sprite suggests instead of larger, as hitting your head on thin air feels horrible) and increase the weight of the jump or add variable jump height to give more control over the movement.
Even despite these complaints, well done on your submission and the creativity! I appreciated what you were aiming for with the epic finale of objects falling from the sky.