That 3rd picture appears to be a different stem. Assumed to be the cold water side. That on still has the backing for the washer and should still seal tightly.
The first on however has lost some of the backing for the washer and of course should be replaced. I suppose that washer Dan shows could work but you likely would have to grind that lip on the end of that stem first.
In the mean time should research name of faucet and possible replacement stem. Maybe take it to a plumbing supply house first to see if they can help.