What is the ruling on making up missed prayers for one who believed herself to be in a state of purity during menstruation due to not experiencing the usual flow of blood, and if making them up is obligatory, should it be continuous or at the times of each prayer?

If blood appears, whether red or brown (kudrah), during the menstruation period, both are considered menses. Red blood is included in the definition of menses, and kudrah during the time of menstruation is considered menses by the majority of scholars.

Therefore, prayer is not valid during menstruation, and there is no obligation to make up the prayers missed during this period.