When we had a dodger installed on our previous boat, I saved some install time(money) and stone sealed all of the many snaps myself. Took 'em out one by one and inserted some sealant in every hole and drove each one back in. Ten years later when we sold that boat the coring passed all inspections and sensor reads with no problem. You would never want to leave such a hole in the deck structure open. Fill with epoxy or similar.Yes, specifically, "snap stud" or "screw snap stud." The one in the picture looks like it may have been for a companionway cover or dodger?
You mentioned that you have several missing, but if you are referring to the two holes that we can see on the starboard side in the second picture, they are supposed to be there. I have always assumed they allow moisture or condensation to drain, but others might know more.