I didn't play through all of the game, but I'm very much liking where it's going. However, there are a number of technical problems along with a couple ideas I have.
1) This game runs at a painfully low FPS on my comp, I'll try to test it somewhere else, but I've seen this machine run flash games well enough.
2) While running into a wall, jumping does not work.
3) You can't walk on top of switches. While this was probably intended, I wholeheartedly disagree with that.
4) The jump mechanic feels horrid currently. It feels incredibly floaty going up, but then matches a parabolic system on the way down. Maybe it's due to the low fps.
5) I've seen the character bug through walls or otherwise do weird things with them (regain vertical momentum upwards after hitting a ceiling, lose horizontal momentum after hitting a ceiling)
-I agree with boybokeh, it doesn't really feel good to have to detach your head to kill enemies at your feet, especially when the controls for the head make it so that left/right don't work on the ground. (it makes sense, but it doesn't feel that great when trying to kill monsters/avoid them) However, I do really really like the separation mechanics and how they interact with the laser -- I could foresee having to juggle the head, start charging the laser, quickly switch to the body and hit a button, then quickly have to fire the laser and move the body to a different switch immediately. With tighter controls and more solid physics, puzzles like those could easily be made and add a frantic air to the game. (having to catch your head in midair would make the player feel like a god.)
-The separation/reparations themselves should have a "juicier" feel to them: particles and sound effects and maybe a (very) small screen shake. Switching should, too, I should feel it when I transition from body to head.
-Maybe you could consider changing physics between just the body and both the body and head combined. Maybe the body jumps higher without the body attached; it could lead to some interesting puzzles.
-The enemies you have in the game are kinda lame. And by kinda, I mean very. I doubt they're final, but they could be a bit more scary, or just have less of them. (why does every level have to be mirrored? it adds nothing to the puzzle)
-The switchy walls/door things don't make much sense. They look like lasers, but they're walls.
-The background is pretty, but the levels themselves are not. Here is what I mean.
(excuse my shitty paintification, I'm at work currently)
-Terrain could (should) be more varied, move the robot through different places and see wildly different things. They don't have to tell a story, and they don't have to make sense (after all, why does that robot want a taco?), but they would make the game all the more engaging.
Looking back, I just absolutely ripped on your game, and I apologize. That's all meant to be constructive criticism, I swear. I really do like your game, it's clever.