Don't know wtf was going on in the story, but I don't think it really matters. Gave me a Cave Story vibe.
I get the feeling the combat is a cross between a side-view shooter and platformer, which is cool. I love space shooters. I think this is a good mix between the two. In that regard, I think the jetpack having no gravity is fine.
Noticed the sword enemies have a rhythm to their attacks, which is key to defeating them. Maybe some sort of obvious telegraph when they're about to attack to help players with the timing? Maybe the sword shines/twinkles right before the attack, or some sound effect.