Is it obligatory to repeat the Dhuhr and Asr prayers after the appearance of brown discharge following the Isha prayer, knowing that the woman performing the prayers had prayed all prayers from Asr to Isha with a single ablution based on the assumption that no istihadah (vaginal bleeding outside of menstruation) had occurred? And what should be done regarding a dry brown piece, of uncertain origin, found on the tissue during external wiping?

Bleeding is not considered irregular (istihadah) unless it exceeds fifteen days. Brown discharge (kudrah) is not considered menstruation (hayd) unless it is connected to it, either before or after. If it is not connected to it, then it is an impurity (najasa) that nullifies ablution (wudu), and whatever it touches must be purified. If the brown discharge is found after the 'Isha prayer, there is no need to repeat the prayers because an incident is attributed to its nearest time, unless it is highly probable that it occurred before 'Isha. There is no need to repeat the prayers of the following day if it is not highly probable that it occurred before 'Isha.