What is the ruling on the prayers and fasting of a girl who used to perform ghusl after the cessation of blood, then a white discharge ("al-qassah al-bayda' - the white discharge") would appear two or three days later, and she did not know that purification occurs upon seeing the white discharge? Are her prayers and fasting throughout all these years valid?

Purity is achieved by one of two signs: the white discharge or dryness. What the questioner did, performing ghusl immediately upon seeing dryness, is correct. She is not required to wait for the white discharge after seeing dryness. Based on this, she does not need to make up any prayers or fasting days that she performed and fasted after seeing dryness. However, if she recently delayed ghusl until she saw the white discharge, she has erred and must make up the prayers of those days. Making them up is more cautious, and it is the view of the majority of scholars.