What should a 14-year-old girl do when her 20-year-old brother accuses her of impurity and not praying during her menstrual period, even though he knows when she stopped praying?

Your brother's statement "You are impure (najisa)" is forbidden, as it is a form of reviling with nicknames and abusive language, and it stems from ignorance. This is because a Muslim does not become impure, and a menstruating woman is not impure. Aisha used to drink and eat with the Prophet, peace be upon him, while she was menstruating. This statement also resembles the practice of the Jews, who consider a menstruating woman impure. Your brother must fear Allah and repent to Him, and he should know that prayer is waived for menstruating and post-natal women.