Hey AV
I looked at your video and you've got a rough road ahead. It can be done, but it is above most peoples skill level.
Parts missing - jaws + screws, lead bolt, dust cap, C plate + screws, maybe a side pin. No base(Might not have come with one).
Broken - main casting jaw holder.
This size of vise does not break easy, and is hard to repair. I would check the main screw to see if it is bent or threads are distressed.
If it were me, I would part it out and look for a better example. The money you spend will never be recouped and unless it is done right the vise will not be usable to its potential. No one will pay top dollar for a repaired vise.
drivesitfar is right about the jaw shelf being a integral part of the jaw support.