Zanorin, I actually tried to give the hood some kind of form using lighting, but as I see it's not the best idea with a picture of this size. Thank you for the edits, the sprite without one color looks much better.
That frame when two feet are on the same level makes sense for me, because there is a similar moment in a walk cycle, but I guess I should redact it a bit.
pistachio, I tried using head bobbing, it seemed to give too much movement. Also thanks you for the tips, just realized that the shoulders are on the same level on all frames, that needs an improvement too.