Is the blood that came down thirteen days after the first menstrual period, and continued for seven days with different characteristics (brown, red, black), considered menstruation or istihadah (non-menstrual vaginal bleeding)? And must prayers be made up for the days that were prayed, thinking it was istihadah, then it became clear that it had symptoms of menstruation?

If the blood exceeds fifteen days and there isn't a separation of thirteen days or more between the two bleeding periods, then it is not all considered menstruation, and the woman is considered to have istiḥāḍa (non-menstrual vaginal bleeding). The menstruation of a woman with istiḥāḍa is what corresponds to her usual cycle, or what is distinguished by the characteristics of menstrual blood. A woman with istiḥāḍa must make up the prayers she missed, having thought she was menstruating.