Is the yellowish-white discharge that appears after the yellow discharge considered purity, or must it be bright white to be considered purity? And must one make up missed prayers if she becomes pure after 15 days from the onset of bleeding?

The white discharge (al-qassah al-bayda') is not the yellowish discharge, and purity (tahara) is not achieved by seeing it. A woman must cease praying and fasting upon seeing menstrual blood. Then, she should perform ghusl (ritual bath) and pray upon seeing purity, indicated by one of its two signs: dryness or the white discharge. If yellowish discharge appears after ghusl, do not pay attention to it unless it occurs during the accustomed menstrual period. If the yellowish discharge is continuous with blood and exceeds 15 days, the woman is considered to have istihada (non-menstrual bleeding). If she ceased praying, believing she was menstruating, when she was in fact obligated to pray, she must make up the missed prayers according to the majority of scholars, provided it does not harm her body or livelihood.