Is it necessary to cover the face or to ask about the child's age when seeing two young children whose ages are unknown entering upon their mother in a Quran memorization school, and when should the niqab be worn in front of them?

There is no need for a woman to observe hijab in front of young boys. However, for discerning boys who have reached the age of sexual desire, the ruling for them is the same as for adults. The criterion is the preponderance of probability: whenever it is highly probable that the boy has reached a stage where he desires women and understands their matters, then hijab becomes obligatory in his presence; otherwise, it is not.