Jonathan i used those machines when i was an apprentice and they were old then as the square headstock models came out so that lathe is at least 45 years old and probably older. It will have not only be used but abused so you should stand back amazed that it is in such good condition.

Re the chuck, small pieces were held and the chucks overtightened so again hardly surprising the jaws are bell mouthed.

You wont be able to SKIM them they need to be ground, obviously you can skim the soft jaws. I would check the fit of the jaw profile in the chuck body worst case a new chuck around £200

Congrats in getting it in.

Phil