Egrets and Oxpickers.
plover
Creatures which clean (or groom) other creatures do so because the debris or unwanted matter from the creature they're cleaning is part of their diet.
The technical way of saying it is clean your teeth, as you scrub them and use a tooth paste (a cleaner) ...then your teeth are clean.
yes
No modern bird has teeth. However, some birds such as geese have serrations on the edges of their bills which are sort-of tooth-like. The serrations to help them whilst feeding on grass.