Are the intermittent brownish discharge that occurred after an strenuous walk, and the spot of blood that appeared after returning, considered Istihadah (non-menstrual vaginal bleeding), or does the Hajj need to be redone?

The brownish discharge (Kudra) that appeared during Hajj is not considered menstruation unless it occurred during the usual period [of menstruation] or was connected to blood. Therefore, the Hajj is valid and does not need to be repeated. As for the drop of blood that appeared after returning, it is considered menstruation if it was connected to subsequent bleeding and their combined duration did not exceed fifteen days; otherwise, it is irregular bleeding (Istihada).