The improvement is spectacular. Personally I'm rather fond of pixel sizes like this, where the face features are not represented (no visible eyes or mouth).
This could totally be the finished character.
If you like your current character design, before you draw more animations you should check that this character size :
- works well for the entire play area (screen size)
- works well with tile dimensions, assuming you're going to use tiled backgrounds : For example if you pick tiles of 16x16, does he need to be able shoot above a crate that's a single tile ? Does he need to be able pass through corridors that are 1 tile high, 2 tile high ? Should his jump height take him 1, 2, 3 tiles above ?
About the run, it's not noticeable at first but the foot that touches the ground moves back 9 pixels when going from image 2 to 3, and then 5 pixels when going from image 3 to 4. (and same for 6-7 and 7-8)
Since these transitions have the same delay, you should try make them identical spacing. This way, when the character actually runs across the screen, you'll be able to pick a speed that makes the support foot firmly planted on the ground, without sliding forwards in some animations and backwards in other animations.