When is the fifteen-day duration of menstruation calculated if it began on Tuesday, 7/6/2022, with pain and a brownish discharge occurring one day before sunset? And is the brownish discharge that preceded the menstruation considered part of it?

If the brownish discharge and menstrual symptoms appear connected to menstruation after a previous period of purity that lasted fifteen days or so, then it is considered menstruation. Anything beyond fifteen days is considered istihada (non-menstrual bleeding). However, if it is not preceded by a complete period of purity, or if it is not connected to menstruation, then it is not considered menstruation and does not prevent prayer, based on the hadith of Umm Atiyyah: "We did not consider the brownish and yellowish discharge to be anything."