When should one stop praying and performing ghusl if bleeding persists, and when should one pray in a state of istihadah, and what are its conditions?

Whatever blood a woman sees during a time suitable for menstruation is considered menses. Recurrent bleeding, if it occurs during a time suitable for menstruation, is considered menses; otherwise, it is considered istihadah (non-menstrual bleeding).

Accordingly: It is obligatory to refrain from prayer for the duration of seeing the initial blood until it ceases with the sighting of the white discharge (al-qassah al-bayda'). As for recurrent bleeding, if the interval between it and the cessation of the previous bleeding is less than thirteen days, and the total days of both bleedings exceed fifteen days, then this recurrent bleeding is istihadah.

A woman experiencing istihadah is obligated to perform ablution (wudu') for each prayer and may pray with her ablution as many obligatory and supererogatory prayers as she wishes until the time for that prayer expires. Then she should revert to her previous habit. Otherwise, she should act based on sound discernment. Failing that, she should estimate based on the predominant habit of women in her family.