Must the aforementioned woman make up for the days she fasted, prayed, and went to the mosque, believing the blood was istihadah, and then it became clear to her that it was menstruation?

If the period between the cessation of the first menstruation and the appearance of the second blood is 13 days or more, then the returning blood is considered a second menstruation. The days fasted during this period must be made up, because the fasting of a menstruating woman is invalid by scholarly consensus. However, if the period is less than that, it is considered irregular bleeding (istihadah). These days must be made up before the advent of the next Ramadan.