Is it obligatory to make up the prayers that were missed because the questioner thought the blood was istihada (non-menstrual vaginal bleeding), even though she does not remember the duration? And if it is obligatory to make them up, how should the duration be estimated?

The blood that appears eleven days after the cessation of menstruation is istihadah (non-menstrual vaginal bleeding), not menstrual blood. This is because the minimum period of purity between two menstruations is 13 days according to the Hanbalis and 15 days according to the majority of scholars. Istihadah blood does not prevent prayer, and the woman is considered pure. She should use a cloth or a sanitary pad to cover the discharge and perform ablution for each prayer after its time has begun. The woman must make up the prayers she missed due to ignorance during istihadah. If she forgets their number, she should strive and err on the side of caution in making them up until her obligation is fulfilled.