Does COVID vaccination prevent infection and transmission?
Both of those factors make COVID vaccination quite different from, say, measles vaccination (~97% prevention, lifelong immunity), and seemingly more similar to the flu vaccine, which is not required by any schools (that I know of).
As to the time the immunity lasts, that remains to be seen. Since it is brand-new, we will only know when new cases from previously-vaccinated people pop up. Maybe it'll be yearly, maybe a booster every 10 years, maybe lifelong. There is research showing that the antibodies from a corona infection last about half a year, but that is not the only factor that may provide immunity. And the yearly flu shot is because the flu virus mutates very rapidly, which corona doesn't as much.