Is it necessary to repeat the fasting and prayer after having performed ghusl and prayed based on the assumption that brown discharge was not menstruation, only to find out later that it might have been menstruation?

When facing religious ambiguities, one must consult scholars. There is a disagreement among scholars regarding the brownish discharge (al-kudrah), but the stronger opinion is that it is considered menstruation if it occurs during the usual period or if it is connected to blood. Accordingly, if the brownish discharge occurs during your usual period or is connected to blood, it is menstruation, and you must make up the days of fasting during which you observed it. If you did not perform ghusl (ritual bath) after its cessation, you must make up the prayers you performed before ghusl, as they are not valid. This is the view of the majority and is the more cautious approach. However, if it is not considered menstruation, then there is nothing upon you.