Roos

Also keep the feed dry and fresh. Damp starter is a separate problem that looks like this one.

Boredom is underrated here. Nine ducklings in a bare brooder with nothing to investigate will investigate whatever is on the floor, and the floor is mostly droppings.

More space as they grow, a shallow dish of water for supervised splashing at a safe depth, and greens to rummage in. Mine stopped almost entirely once there was something else going on in there.

Deep enough to get the whole bill in, yes, and that is a real requirement rather than a nicety. Blocked nares cause their own problems. But not deep enough to climb into and get chilled or drown at that age, so put stones or marbles in a dish rather than giving them an open bowl.

Right after eating and drinking, with head shaking, in birds that are otherwise loud and busy is the normal version. Their nostrils are on top of the bill and they dunk specifically to rinse feed and dust out of them. The sneeze and the head shake are the rinse finishing.

Crumbly starter feed gets up there, so does dry bedding, so the two moments you noticed are exactly the two you would expect. Five out of five doing it is not a cluster, it is five ducklings with the same bill.