Is a woman considered pure and can she pray and fast while experiencing continuous brown discharge, which coincided with taking medication to delay her menstrual period during the last ten days of Ramadan?

Brown discharge (kudrah) is considered menstruation if it occurs during the usual time of menstruation, or fifteen days after the last period of purity.

Therefore, if this discharge appears at your usual time of menstruation, it is considered menstruation, and you must break your fast and make up for those days.

Using pills to prevent menstruation is permissible, although it is better to avoid them.