Thanks for all the nice and useful comments!!!
I forgot to mention that the jumping was a messy 10 minute test. I am not even sure yet how high I want him to jump, which is important for the animation I guess. The jump will be fully remade, and the stuff you guys wrote about that will help.
Also, I was aware that the arms were not perfect, but I did not know how to make them like that. Thanks to souly I do now!
Willfaulds, thanks for noticing that leg, I fixed it as soon as I read that!
No, it is not a roman outfit. I hope it is all obvious when I say that it is a fat caveman/stoneage kid?
Here is the new version of the run animation
EDIT
2 modifications. Tell me what you think of them. Oh and btw, the game is supposed to be a bit funny, humor style, so I will have to bring more humor in my sprites if possible.