He looked like he was running backwards to me as well. Upon further inspection, he is running backwards. I downloaded the gif, and the first and last frame are swapped. Here's what he looks like running forwards.
I think his front leg looks a little awkward because there is a block of 4 squares or so that really look like they're not moving.
I think what you really need is one more frame that transitions his front arm and front leg so it's not snapping between these two frames.
As for the style. It really depends on what you want it to look like. I could imagine a game that has this kind of sprite style in it. Without seeing more art from the game, it's hard to give an opinion.
Good job!