Possible, but not always the easiest option. Especially if sheared off with nothing left to grab on to. A little heat applied will help it get through the plastic - again, if you can grab it. With that one sheared off like that, I would probably remove all the solder on the reverse side and use a pair of side cutters with a light grip to pull it back through. I think the easiest source for a pin is a scrap board, I've never ordered the pins themselves, so I can't tell you much about that.

You might be able to cut the last two off including the plastic and then desolder them separately. Are you sure they snapped it off and it's not just keyed like that?

Ditto!

No other pin is missing?

Ribbon cables aren't USUALLY keyed on the edge like that...usually in the middle....but...look at this schematic. Pin 20 goes to NOWHERE? Also, the pin below looks bent. It's probably best to just carefully clip the plastic and replace both of those at the same time, but I dunno... if those are .100 pins, might be difficult to find a 2x1. Likely would need to buy a bigger one and cut to size. When in doubt, look at the ribbon cable itself. If it's keyed, that hole will be plugged or not even there on the connector, so that's an easy answer.

LaserWar-CN21 (resized).png

That's pin 1, and it is ground so it is needed. If it had been pin 20 on the opposite side it wouldn't matter, as pin 20 is N/C.

in the time we've talked about it the whole header could have been replaced.

Thanks for clarifying that too. I wasn't exactly sure how that connector was numbered. These schematics/manuals are so godawful compared to Williams Sys11/WPC. Ugh.

Can't really fault the guy for wanting to do LESS board work if he doesn't feel particularly comfortable with it? That's better than doing the whole thing and blowing out 10 traces..

True, but we all know that sometimes cutting corners backfires, and you end up having to do it right in the first place.

Unfortunately, that is actually pin 1 that is broken.
You can see a "19" and "20" to the left of the connector in that photo. That means pins 1 and 2 are at the opposite end of the header.
There is a nice diagram showing pin numbering and signals in the user manual as shown here:

CN21 (resized).jpg