This is a summary in our own words. The text that applies is on wetten.overheid.nl.
Yes, if the seat has a seat belt and the child is three or older. That's in article 59a of the Reglement verkeersregels en verkeerstekens, the Dutch traffic regulations, and it applies to the driver and to every passenger.
No. The rule of a child seat up to 1.35 metres is in article 59 and is about cars. On a bus a child seat isn't compulsory. If you want to use one anyway, ask the coach company whether it fits their seats.
Yes. Passengers under three are exempt on a bus, even if there are seat belts. They don't need their own seat either.
The law names the driver, the conductor, the tour leader or an appointed group leader, and also an announcement, a sign or a pictogram on every seat. For a school trip, agree in advance who will do it.
Then everyone may sit without one, adults and children alike. If you want to be sure there are seat belts, put that in your request so the coach company can take it into account.
Fill in your place of departure, your destination and your group, and compare the coach companies with their prices.