I've been thinking about it a lot, and after reading what >>37872 said, I think the reason that the characters look like they're floating is because we -as, the audience/players- keep expecting the shadows to work like they would in the Zelda screenshot: as simple shadows beneath the characters, but because you're using them as side-shadows, it clashes with the expectation we have, and our brains go all "no, no, it has to be the shadow beneath them! They must be floating, then!", even when it doesn't really make sense.
I wish I could help with the sprites and music, but those are simply things I don't know how to do. :(
You might want to add a post saying that you need help, with attention-grabbing bolded text, so people scanning through collab can see it, and hopefully a pixel artist and/or musician will decide to help.
I also feel kind of a hypocrite bringing it up, but I think that adding a little texture to some of the plainer tiles would help a lot. Compare the grass in the screenshot of the very first post here, to the tiles of the castle or the lava room, and the first one looks better.