Is the fasting and prayer of a woman valid if she suffers from a blood fluidity that led to bleeding that lasted for more than 13 days, and the doctor confirmed it was a hemorrhage?

The maximum duration of menstruation is fifteen days. So, if the blood continues for fifteen days or less, it is menstrual blood, necessitating the making up of fasts but not prayers.

If the blood exceeds fifteen days, then the woman experiencing it is considered to have Istihada (non-menstrual vaginal bleeding), and her menstruation is determined by her usual period each month. If she does not have a usual period, but can distinguish menstrual blood, and it is not less than one day and one night, and does not exceed fifteen days, then she should refrain from prayer and fasting during this period.

If she cannot distinguish the blood, or distinguishes it for less than one day and one night, or for more than fifteen days, then her menstruation is six or seven days, based on what is common among her female relatives. After that, she should perform ghusl (ritual bath), and then fast and pray.