Oh yes, well done, the run sequence looks much more natural like this!
It's hard to tell for a jumping animation. Usually, running sequence are quite similar because the point of running is usually to reach a high speed and there are not a lot of equivalent and really effective ways to achieve this for a human. But when you jump, there are many possible goals. Examples: Are you trying to vault over something while not losing speed? Are you trying to reach high? Are you trying to reach a maximum distance? Do you jump from a running or walking or standing start? All of these things will affect a jump animation.
For LoK:R I tried to make a jump sequence that would more or less fit with all of this but focus on what would happen most often: which is try to reach high from a running start. Which is, by pure coincidence, something I do in taekwondo (for jump kicks). So I had a good idea of the body mechanic behind this jump. In such a jump, to reach high, you must launch one of your knees very high while the other leg is extended to push from the ground as long a possible... Hum, it's unfortunate, I can't find a good picture of this. Anyway, when you go near the apex of the jump, the legs begin switching position: the high knee is lowered and the extended leg is retracted back near the body. When getting near the ground, the extended leg is not the first leg to make contact with the ground since it is now higher than the leg taht was initially launched in the air.
In your jumping animation, I see 2 images. One image when going up and one when going down. The first issue I think is that these images do not really suggest movement. The image of "going up" should show a position suggesting a push on the ground, the image of "coming down" should be an image of bracing for impact on the ground. If you could insert an image for the apex of the jump, wou could make a smooth transition between your two jumping images and make more "extreme" stances for pushing the ground and landing on the ground. In LoK:R, during a jump, I check the vertical velocity of the character. Whe it is near 0 and the "jump" flag is on, I switch to the jump apex image. When the "jump" flag is on and vertical velocity is going up but not near zero, I use the push the ground image, and of course, if the jump flag is on but all the rest is false, I use the landing image.
Hey! I found a video showing a jump side kick. Of course the landing and the apex of the jump aren't what you want since there is a side kick in it, but there is a slow mo in the video which will allow you to see the initial image (knee launched high and leg extended to push the ground). From a running start and trying to reach high, I think it's pretty good.https://www.youtube.com/watch?v=Kai2SSYQ9lg
I hope this helps.
Keep up the good work!