First of all, thank you for playing our game and giving your input on it!
Falling of the edge is intended, but maybe it happens too often as the map size is too small in later levels. Also, landing on the cube bounces the player off too much I think.
I agree that the punching mechanic needs tweaking based on the reasons you provided. We also planned to make ranged weapons, like a laser to burn eyes with, but didn't manage to in time.
You're also correct about the powerups. After clearing a wave/level you have the choice to pickup the powerup or continue without it (as it can either buff or nerf the player). We also had the option in mind you suggest: hand the player the powerup and he has to adapt. I agree this would have been better, also as it suits the out of control theme more.
Thank you for your thoughts on it!