Is the reddish-brown discharge that appears after a day or more of dryness following menstruation considered menstruation, requiring waiting and ensuring purity afterward? And is ghusl obligatory every time a spot of doubtful color appears between periods of purity, especially if it does not appear after the fifteenth day?

A woman recognizes the end of her menstruation by one of two signs: dryness (al-jufūf) or the white discharge (al-qaṣṣah al-bayḍā’). Once she sees the sign of purity with either of these, she must perform ghusl, and all rulings applicable to pure women apply to her. If she then sees blood again at a time suitable for menstruation, she reverts to being in a state of menstruation. As for yellowish or brownish discharge (ṣufrah and kudrah) after purity, it is not considered menstruation unless it occurs during her regular period. If you have verified your purity and then doubt the return of blood, the original state of purity remains. If you are menstruating and doubt your purity, the original state of menstruation remains until you verify its cessation. If you see dryness, you are pure. If you then see brownish discharge mixed with blood, it is menstruation until it ceases. However, brownish discharge alone is not considered menstruation except during your regular period.