Hey; thanks for playing.
The gust ability only comes online later (after you beat the boss), but it is the double jump, so you probably have been getting it right. You need to hold up when pressing B / shift. I modeled the control scheme after Super Smash Bros.'s up special moves, but I think it might have been a bit tricky to pull off properly.
Though I didn't manage to complete a lot of content, so once you have the gust ability, there's nothing else to do, so you're probably done.
Regarding the resolution, I didn't even think to test that! I was hoping the "scale with screen size" setting would sort that out. Thanks for pointing it out! I'll see if I can figure out how to fix it.