Thank you so much! <3 Also, completely agreed that a little movement of the head/torso would keep things looking a little less rigid. Fabulous detailed criticism, much appreciated!

 I agree with toxotes, you have a good start here! One thing that woud help the running/walking animation to look beter would be to make her torso go a little up on the middle frame, the "passing" one where the legs are together, and a little down on the frame where the legs are apart from each other. Like this http://killanument.com/wordpress/wp-content/uploads/2012/05/WalkCycle_Side.jpg but only taking the middle drawing and the ones on the extremes if you want to keep your sprite with 3 frames for walking. This will help the movement look more natural and less stiff. 

 It's a good start, but these could definitely benefit from a few more frames to smooth out the animation.