Is the blood that comes down after the cessation of menstruation, and whose nature changes between brown and red, considered menstruation that prevents prayer and intercourse, or what?

The fundamental principle is that any blood discharged by a woman is considered menstrual blood unless it exceeds the maximum duration of menstruation – fifteen days according to the majority of scholars – or if it persists for most of the month, in which case she is considered to be experiencing irregular bleeding (istihadah (definition)). Yellowish or brownish discharge (sufrah and kudrah) is considered menstruation if it appears before the sign of purity (tuhur), but it is not considered anything after purity. The signs of purity are the discharge of white fluid (al-qassah al-bayda') or complete dryness. The menstrual period may increase, decrease, or be interrupted.

Based on this: 1. If the sign of purity appears after the first few days, then any yellowish or brownish discharge thereafter is not menstruation, but blood is. 2. If the sign of purity does not appear, then yellowish and brownish discharge is menstruation. If blood persists for most of the month, you are experiencing irregular bleeding (mustahadah). A woman experiencing irregular bleeding should refer to her regular habit if it is stable. Otherwise, she should differentiate based on characteristics (color, smell, and consistency). If she is unable to differentiate, she should estimate six or seven days as is common for menstruation.

In summary: Blood is menstruation wherever it is found. Yellowish and brownish discharge have specific details. A woman experiencing irregular bleeding (mustahadah) is one whose blood, or blood connected with yellowish and brownish discharge – without seeing the sign of purity – persists for most of the month.