Great atmosphere and mechanics! I can see really cool stuff with the jump/swap but I find it a little bit too crowded with obstacoles. Got to the third level and while I really dig finding solution and then perform it I felt a bit too much of step curve and no rest from the already hard (but really great) 2 levels. Will give it a go again for sure!
Hiya! For the third room, you're looking to teleport as soon as you bounce on each springblock. That'll send you upwards from the green orb, letting you drift back down to activate the others until you can get past them. If you haven't, I'd recommend trying the original game to get a feel for the mechanics in their original usages :) And downloading can help as well, as sometimes playing in browser can cause some sluggish responsiveness for controls.
Good luck!