Thanks for playing! :)
"Up" is just one option to jump, you can find the others in the description of the game. I think a gamepad is the best choice anyway, but for keyboard I'd prefer "alt-gr" to jump. EDIT: Tested again; somehow I did'nt realize that "alt-gr" seems to only work in the download-version. Another alternative for jumping would be "w" though.
You can jump a bit higher if you hold the button longer, also you can use the attack to get even higher while in air.
You can't be softlocked in the first valley, I've tested everything so you'd be able to make it up there without the bubbles.
Regarding the fullscreen: Well, I don't know. I just used it like Unity gave it to me. There's no code from me for this, so I'll have to google it myself to find an answer.