Are feces-like discharges, in small quantities, that exit from the anus and are seen on underwear considered among the minor impurities that are pardoned? And does the ruling differ if they exit before or during prayer?

If the discharge is rare, it must be washed, and whatever of it has stained the clothes must also be washed. If it is found after the prayer, the default assumption is that it exited after it, and the prayer is not invalidated, unless there is an indication that it exited before it. However, if one prayed with it while knowing of its presence, the prayer is invalid. If the discharge is abundant and continuous, it takes the ruling of perpetual impurity ( سلس).