I like that the new tiles are cleaner and don't feel as noisy.  They were quite distracting before.
The skeleton color tone could maybe go a light gray to shaded blue(maybe?) to help differentiate the sprites more.  The yellow/orange color didn't read immediately as bones to me.  Gray would probably blend too much with your already gray elements but if you go highlight and move towards blue in the shade it might stand out in a fun way.

@ Alp
It's in mind.
I did some 16x16 retro play a month or two ago and it turned out to be a great learning experience. I have found that limitations are usually better for learning than giving yourself unlimited resources. When I said that there was only so much you could do with sprites that were so small, I only meant that it's not as easy to apply "rules and concepts".  And by that I mean that the smaller you go the more interpretation you use on shapes and form.  It's harder to criticize the technique used in those cases.
Poor choice of words on my part and I own that. No harm done in calling me out on it.   

There is only so much you can do with sprites that are so small.  Critiquing these are a bit difficult because of that.
You have bits of color that are very close together as in the two gray's on the shirt and the tones on the head.  If you widen the contrast between those colors they will stand out more.  Also the black lines you are using on such a small creation will make them seem even smaller.  Attempt to use a much darker version of a similar color as the content of the sprite.  For example: DARK gray border on the shirt instead of a black line.

Just some thoughts:
What I am seeing is that the arms flow fully in front of the body with each pump but the legs only appear to reach straight down to the ground.
That coupled with the heels and lower legs moving up parallel to the ground gives a sort of running in place feel.
The arms are swinging super wide too.  It looks awkward because I think if you tried to run this way you might fall down.  I think it would take someone with good balance to manage a run like this and it would be uncomfortable.

The skirt also conveys a sort of flopping back and forth of her balance because it swishes so vibrantly to the sides.  I'm not sure running would make a skirt flop back and forth this way.  It seems more logical that it would billow slightly outward as the wind kicked it up in the back.

The more I look at this the more it looks to me the way a person runs in the water.  Arms wide to keep balance against something dragging their legs down.  Legs not moving as far because they are meeting resistance.  Exaggerated steps on each side to drive body forward against that resistance.

Maybe it will help.  Animation isn't a strong point for me at this time.

This thread continually reminds me of this scene from Jurassic Park.
Maybe her body motion can help...
https://www.youtube.com/watch?v=PscRUlsvhtI#t=166

She is sorta running and I feel as if it is fairly exaggerated, but it's not an unbelievable performance.