Is fasting permissible on the first two days of brownish discharge, which occurred eight days after the end of menstruation, keeping in mind that the normal menstrual period followed it?

This brownish discharge is not menstruation because it is neither within the customary period nor connected to blood. The prayers that were missed during that time must be made up. As for the fast, it is valid and sufficient, and there is no need to make it up.