Elf on the Shelf is recent and commercial; no problem if a family WANT to do it and find it fun, but no need.
Christmas Eve boxes I think have older roots - growing up abroad, my family used to open any presents from family overseas and whoever couldn't be with us on the day on Christmas Eve, and some families with small children have always done the "open one present on Christmas Eve" to manage overexcitement. But buying extra stuff and putting it in a special "Christmas Eve box" is recent and commercialised; many people don't do it.
Stockings, I think, are pretty standard but may not be missed if stocking-type items are mixed in with the regular Christmas gifts (that is, not just one big gift per person). A lot of parents find it HELPFUL to do stockings as it keeps the children occupied so they're not up wanting to open main presents at 5 AM.
Visiting Santa can be fun for little kids, and there can be sentimentality around pictures of the visits, but a lot of people live places where this would be tough.
Leaving anything for him or his reindeer, footprints etc. Totally optional, and a step too far for some people who are uncomfortable with the whole Santa/Father Christmas deception.
Gifts are from the people that bought them, no gifts from Father Christmas he is just the delivery guy. As above, but I'd just ignore FC/SC in this case.
Christmas Eve church service - many families skip this especially if not religious (or observing Christmas as a cultural holiday but no Christian background).
Buying teachers gifts may depend on what's normal/expected where you live. It's always optional. I can see a child being uncomfortable feeling like the only one not to give a gift, but this seems unlikely.