Is the fasting of a woman experiencing a continuous discharge of brown and red secretions, then light bleeding and secretions after it stops, valid, knowing that she is taking medication for that?

The returning blood on the the seventeenth day is considered menses as long as it falls within the potential period of menstruation. If it stops before April 20th, then perform ghusl and make up the days you fasted during that period, because your fasting during it is invalid. However, if the blood continues after this date, then you are experiencing istihaadah (non-menstrual vaginal bleeding), and you must follow the rulings of the mustahaadah. Your fasting on the days of purity that intersperse the two bleedings is valid.