Hm, I'm not sure you got it and now some of the movements are weirdly slow on the first few frames.
What I meant was more leading with the hand, having it move from the box to the left a bit then back up to where his "mouth" would be.
The MOTION on the box grabbing hand is better, but try to fix that frame pacing.
As for the slight turns of the head, try some subpixeling concepts like this:
This isn't the BEST done example on earth, but it showcases the concept. The idea is to use changes in color inside the sprite, rather than the edge or profile of the picture, to create the illusion of smaller movements.
Metal Slug uses this concept to great effect, if you'd like more professional examples of the technique!