Okay. First of all, are you sure you've got the perspective right? You describe this as "top-down", and I suspect you actually mean the traditional 3/4-ish view used in 2D JRPGs, but when I look at the art, it seems more side-on than it should be. Or maybe it's just that I'm expecting chibi proportions. If it looks okay in the context of your project, just ignore me.
Secondly, coloured outlines are fine, although multi-coloured outlines add to the amount of effort you need to animate (since any detail increases animation difficulty). The purpose of an outline is to get the sprite to stand out against a background. If it does that well enough, it doesn't matter whether you have a black outline, a coloured outline, or no outline at all.
I'm far from a master of animation, but I did notice a couple of things. On the first frame of the forward diagonal animation, the far leg looks almost like it's sticking out to the side. It's something about the shading, but I can't put my finger on it better than that. Also, in the same animation, the hand of the near arm seems to come further across the torso than the far arm. Part of that is perspective, though. And he looks like he's looking slightly toward the camera, rather than straight ahead in the direction he's moving.
Side animation: Feet seem to vary in size more than perspective+shifting weight would account for. Highlight on the near leg is maybe a bit much.
Rear diagonal: The legs here just are not quite right. I get the impression that he's trying to move more "into the screen" than the angle of the head and torso suggest, and his legs should be getting tangled at the ankles and making him fall over. Frame 4 in particular just makes him look off-balance.