Is ghusl required upon seeing white discharge after menstruation has ceased? What is the ruling on the prayers performed during the two days after ghusl? And is the brown discharge that appeared later considered part of menstruation?

It is not permissible for a woman to delay performing ghusl after seeing the signs of purity, and she must make up the prayers of the day on which she delayed ghusl. As for the brownish discharge (al-kudrah) after the cessation of menstruation by more than two days, it is not considered menstruation unless it occurs during the days of her usual period, and your prayers during that time are valid. The yellowish (al-ṣufrah) and brownish (al-kudrah) discharges are not considered menstruation except if they occur during the period of her usual custom or are continuous with blood.