How is one to be certain of the cessation of menstruation, and are brown or yellow discharges a sign of purity, and what is meant by inserting a piece of cotton into the vagina to ascertain purity?

"Yellowish and brownish discharges connected to menstruation are considered menstrual blood, provided their duration, along with the blood, does not exceed fifteen days. Purity is only recognized by seeing dryness, the criterion for which is the cotton swab emerging clean, with no trace of blood, yellowish, or brownish discharge, or by seeing the white discharge (al-qassah al-bayda’). So, if the cloth or cotton swab comes out clean, she has become pure; otherwise, she remains in menstruation until she sees dryness."