After I have gotten a new move I wanted to go back to the very beginning of the game.

However, in "Plane cockpit" I got stuck. Is there a way to get back? All I can do is jumping in the cockpit where I can't do anything. Is the door in the cockpit supposed to be opened? Or do I get back later in the game from another direction?

Any help is appreciated, thanks in advance.

You can go back through the same window you came in( the one you smashed with sweepkick). Try it a couple of times, it's tricky but eventually you'll get it.