Was intercourse during the sighting of blood forbidden? And what is the ruling regarding the wife's prayer under the aforementioned circumstance?

Your wife is a woman with irregular bleeding (mustahadah) as long as the duration of the bleeding exceeds fifteen days.

Rulings for a woman with irregular bleeding (mustahadah): 1. Knowing her regular period: She refers to her previous regular period if she knows it. 2. Discrimination: If she does not have a regular period, she acts according to sound discrimination (characteristics of the blood). 3. Prevailing opinion: If she has neither a regular period nor the ability to discriminate, she considers six or seven days as menstruation based on investigation, and anything beyond that is irregular bleeding (istihada).

Rulings on intercourse: During irregular bleeding (istihada): Intercourse is permissible during the time of irregular bleeding according to the majority of scholars. During previous menstruation: If intercourse occurred during her menstrual period due to your ignorance, it is hoped that you both will be excused. Going forward: You are not permitted to have intercourse with her during the days counted as menstruation, but it is permissible during the days counted as irregular bleeding (istihada).