Must a woman make up the days of Ramadan that she fasted, thinking she had become pure, while the brownish discharge was still considered menstruation? And what should she do, and how should she make up her fasting, and should she give charity for every day she did not fast?

The brownish discharge during menstruation is considered menses. Therefore, a woman's fast while experiencing this is invalid, and she must make up those days. She is not required to give charity for the days she fasted, as the Ummah has unanimously agreed on the prohibition of fasting for a menstruating woman and that her fast is not valid. As for prayer, she is not required to make up her prayers.