Are the intermittent bleeding after the first four days of menstruation, and the brown discharge, then the light red blood that tends to be brownish, then the yellowish-white discharge, and the presence of white discharge on normal days, signs of purity or not, and what is the validity of fasting in this case?

The fundamental principle for the cessation of menstruation and the commencement of purity (tahara) for a woman with a regular period is the sighting of the "white discharge" (al-qassah al-bayda'). If she does not see it and finds red, yellow, or brown discharges after the bleeding has stopped, she should not consider herself pure until she sees it. Aisha, may Allah be pleased with her, used to tell women: "Do not rush until you see the white discharge." Purity is also known by "al-jufuf" (dryness), which means that a woman inserts a piece of cloth into her private parts and it comes out unstained by blood. If neither dryness nor the white discharge occurs, the woman is still considered to be menstruating, and her fasting is invalid, unless her menstrual period exceeds fifteen days. If dryness occurs, the woman is pure, even if brown or yellow discharges appear afterwards, provided that the dryness occurs after the usual days of her period have ended. However, if the bleeding stops without complete dryness, the mentioned discharges are considered remnants of menstruation. Yellowish and brownish discharges are considered part of menstruation if they occur during its usual time. It is recommended for a woman whose habit is to become pure only by the white discharge, or by both dryness and the white discharge, to wait for the white discharge until the end of the chosen time (for prayer) so that she performs the prayer in its last part.