How do I create these hybrid photograph videos? Only some parts of the photo are moving.
Risking to state the obvious: those are animated gifs. Considering their limited colors and big sizes at even relatively low resolutions you'd try to change as little as possible between frames of the animation.
My guess is these gifs are based on video footage with some clever and careful masking; only a portion of the images actually change.
You can see this if you look at the arm of the man in your last example. you see the arm stops moving at the elbow. Hair is more difficult to track (too many lines that distract the eye easily).
I would first find suitable footage then export the second or so that interest you as stills
You probably could work well with as little as 12 frames/second.
Get that images into a program that can handle animated gifs. In photoshop (CS4, CS5 you can switch your workspace to "Motion").
The difficult part is to create a good loop. There are tricks like using some previous frames to "return" the animated parts close to their original position in order to make the loop less choppy. also (motion)blurring or recreating the parts by painting over etc are valid tricks to get the end of the animation to line up again with the beginning.