When should one perform ghusl and pray if the menstrual period is prolonged and the white discharge (al-Qassah al-Bayda’) is not seen until after a long time? And do daily moisture and white discharge invalidate ablution, regardless of their color?

If the days of bleeding exceed fifteen days, then you are in a state of istihadah (non-menstrual vaginal bleeding), and you must refer to your previous habit. Once that period ends, perform ghusl (ritual bath) and pray, and you will have the rulings of pure women. If you do not have a previous habit, then rely on distinguishing between menstrual blood and istihadah blood by its characteristics. If you have neither a habit nor the ability to distinguish, then observe six or seven days as menstruation each month, based on careful estimation, then perform ghusl. During the days of istihadah, perform wudu' (ablution) for every prayer after its time has begun. As for discharges, they invalidate wudu' but are pure and do not necessitate istinja' (washing of private parts) or washing the garment.