Thank you for such a thoughtful feedback!
Ice puzzles are usually constant: the player cannot change the placement of the ice. Even if the player can, it tends to feel pretty "rigid". The shadow system in my game gives the player much more freedom and the solution to a puzzle therefore become much harder to find. The game already has lots of potential with the current set of mechanics, and I still have a handful of toys that I left out due to the time constrain of the jam, so maybe I will implement some of them in the future.
The controls aren't a little frustrating, they are straight up ruining the fun of the game, now that I saw so many comments about them. When developing the game, I already knew the solution of the puzzles so I just pressed keys with lightning speed and didn't feel anything weird about them, so I learned a valuable lesson here. I didn't implement the diagonal movement because that will double the work needed to make a puzzle since there're double the normal amount of direction the robot can move, and I have to be even more careful while constructing a puzzle (which is time-consuming). I may implement it in the future as well.
You are right about the hitbox of the player, it will have been much better if I let it be a 1x1 square, rather than some wonky rectangular shape as it is right now.
For the last room, of course you aren't supposed to cheese. I will try to cheese like how you described when I have the time, but for now, I have a full gameplay video so if you didn't watch it and still wanting to see the official way to beat the level, head over to the game's page.
Once again, thank you for the thoughtful words!