@kill
You can't press spacebar because that's a forcefield only YOU can go through. Pressing spacebar in there is impossible, because the clones wouldn't be able to do it, and that move would do nothing. It's a nice catch by the dev(s).
On the last stage, just keep running to the right and jumping. Press space at random times during the cliff. You will eventually jump on a past version of your self, therefore 'double jumping' over the cliff.