Must a woman make up the Fajr prayer if she sees purity a few minutes before Fajr and finishes ghusl after the time for prayer has ended? And must she make up the prayer of the previous day if she saw white discharge and doubted whether it was the white discharge indicating purity, and did not perform ghusl fearing to fast while impure?

A woman knows she is pure by two signs: dryness (the cotton comes out clean), or the white discharge. As soon as she sees purity, she must perform ghusl (definition) immediately and will have the rulings of pure women. You are required to repeat the prayers you missed after seeing purity and before performing ghusl. As for the dawn prayer, it is not obligatory to repeat it.