Words to describe a person who frequently asks questions even though they know the answer
Solution 1:
Didactic as defined by Google: in the manner of a teacher, particularly so as to treat someone in a patronizing way.
Solution 2:
wiseacre
A person with an affectation of wisdom or knowledge, regarded with scorn or irritation by others; a know-it-all.
Another choice, that's an Americanism is
wisenheimer
A person who behaves in an irritatingly smug or arrogant fashion, typically by making clever remarks and displaying their knowledge.