Is it obligatory to make up prayers that were missed due to a mistaken understanding of the methods for ascertaining purity (dryness and the white discharge), and is there sin in persisting in this mistaken understanding after the first menstrual period?

A woman remains in a state of menses until she verifies purity by one of its two signs. If she sees purity, she performs ghusl (ritual bath) and prays. If, after that, she sees yellowish or brownish discharge outside the time of her usual period, it is not considered menstruation. As for past prayers she missed, thinking she was menstruating, there is a difference of opinion regarding the obligation to make them up. The purity that occurs intermittently during menstruation is a valid purity. So, if she sees purity, performs ghusl, and prays, then the bleeding returns, she reverts to being a menstruating woman if it is a time suitable for menstruation. What she did by praying after seeing brownish discharge outside the time of menstruation is valid.