When should a woman perform ghusl, fast, and pray if bleeding continues for two days after childbirth, followed by a brownish discharge, then light brown discharge that is almost yellowish, given that her usual period was 9 to 10 days and she did not see the white discharge?

The yellowish and brownish discharges connected to blood are considered menstruation. The fundamental principle is that you remain in a state of menstruation until you observe purity through one of its two signs (dryness or the white discharge). However, if the duration of the blood and its connected yellowish or brownish discharge exceeds fifteen days, then you are experiencing abnormal uterine bleeding (istihada).