Are brown discharge or red blood appearing upon inserting a finger, after seeing the tissue clean and white, considered part of menstruation? And is the method of inserting a finger relied upon to confirm the end of the period, or is wiping with a tissue sufficient?

The decisive factor regarding a woman's purity is what she sees on the outer part of the vulva, which is what becomes visible when she squats for her needs. If she inserts a piece of cloth and it comes out clean, with no trace of blood, yellowness (ṣufra), or a brownish discharge (kadira), then she is pure and should perform ghusl (definition). What is inside the vulva is not taken into consideration. If blood reappears within the possible period [of menstruation], she reverts to being a menstruating woman. However, if yellowness or brownish discharge reappears outside her usual period, she should not pay attention to it.