Ah that's weird that the mouse doesn't work for you. If you played the Webgl version make sure your mouse is locked in the screen, if the issue then still occurs then maybe try out a build version like the windows or the mac version.
As for the warping back, it happens when your battery runs out (The big blue bar on the back of the robot). This makes sure you have to get to the next checkpoint in a certain time. This mechanic shines in the last area (third area) where the puzzles make better use of this.
Anyway sorry for the bad experience, sadly i can't help more with the mouse issue other then this info since it works for everyone else weirdly enough.