This is really impressive! Definitely the most game-y I've seen among the entries so far. I really like the idea of having this separate sandboxy tutorial area first to get people to understand the controls.
The puzzles themselves are neat, though just from a personal-preference standpoint, I would prefer the various tiles to snap to a grid or something. But I just like my puzzles to be a little more rigid than completely free-form physics puzzles (because in the latter it can sometimes be hard to tell whether your solution just doesn't work, or whether you just didn't execute it well enough). Still a neat game and I also really like the puzzles sprinkled throughout.
Maybe the multitool could see a little more use. I'm pretty sure in the first room I didn't even pick it up at all. Though to be fair I didn't play all the way through, so I can't say whether it becomes more central to the puzzles later on.
Keep up the good work!