How do I repair a wooden door's hinge binding?
I think it's time for a new door.  

The yellow thing is a wall anchor, and it's not intended to be used here.  They're for screwing into plaster or drywall.

The door is cracked through the screw holes, and any attempt to repair it is just going to make the problem worse.  

Had the door not been cracked, you could drill out the holes and glue in a dowel.  But in this case, you will split the door further when you screw in again.

You could salvage the door by removing it, gluing and clamping the crack overnight and then re-mounting the hinge at a different location.  But any attempt to reuse that mount point will simply re-split the door.