How can a woman know that she has purified herself from menstruation if she does not see the white discharge, and after performing ghusl, she finds brown or black blood descending, and what is the ruling on this blood?

Purity from menstruation occurs with one of two signs: the white discharge (al-qassah al-bayda') or dryness (al-jufuf). Not all women are required to see the white discharge. The purity that intersperses menstruation is a valid state of purity. Therefore, a woman must perform ghusl (ritual bath) and pray upon seeing purity by one of its signs. If she sees blood again, she returns to being in a state of menstruation. What you are doing by waiting after seeing purity is incorrect; rather, one must hasten to perform ghusl and fast. Your fast is valid as long as you do not see blood during the day. If blood returns after that, even if it is a small amount, you return to being in a state of menstruation, and ghusl becomes obligatory again. As for yellowish or brownish discharge after purity, it is considered menstruation during the accustomed period but not at other times.