Quote: Third from the left is, as International3414 indicates, a stud remover, clamping down on the stud to pull it and destroying the exposed stud threads in the process.
Really, I would never had guessed that, would like to see it in action to get a clearer idea
Take a bolt - 3/8" would be about right, from the photo - and insert it in one of the holes, from the bottom (the bottom being the side visible in your photo). Then use the female drive on top to move the knurled wheel into the bolt. With a little experimentation, you'll see which way it would need to be set up to clamp onto a stud. You then just exert pressure with a square drive handle of some kind until the stud comes out (or breaks off below the surface, always fun).
There's another design that uses a wedge. This design's easier to use, when you have the (not inconsiderable) room needed to make it work.
No certain idea on the new stuff you posted, but the puller looking thingie is for some light-duty pull. Not sure exactly, although given the tie rod adjuster that you've posted on another thread, I'd wonder if this is some kind of puller-remover for tie rod ends or similar parts. But I'm speculating like a Dutch tulip buyer here.
