What is the ruling on prayer and fasting for a menstruating woman from whom a brown discharge exits two or three days before her period, then stops, then light bleeding comes for two days, then her normal period for three or four days, then the bleeding stops for two days, then returns again for a full day, light and light in color?

The brownish discharge (Kudra) before menstruation is not considered menses. One must perform Istinja' (cleansing) from it and Wudu' (ablution) for prayer. However, blood itself is entirely menstruation, whether light or otherwise. As soon as it is seen, one must cease praying and all actions that a menstruating woman abstains from. Upon seeing purity (dryness or white discharge), one must perform Ghusl (ritual bath) and pray. If the blood reappears on the same day, you revert to being in a state of menstruation and must perform Ghusl after its cessation. The purity interspersed within this menstrual period is valid, and prayer, fasting, and all other acts of worship are permissible during it. There is no need to make up for the fasting performed during this interim purity; only the fasting from the days when blood was seen needs to be made up.