Are the dark brown discharges that appear at the time of menstruation and continue for four days, accompanied by back and abdominal pains, considered menstruation that prohibits prayer?

If the discharge occurs at the time of menstruation, it is considered menstruation. This is the view of the Hanbalis. So, if you see this brownish discharge during your customary period, it is menstruation, and you must make up the days on which you saw this discharge during your customary period. As for what occurs outside the customary period, it is considered istihadah (definition) (non-menstrual bleeding), which necessitates fasting and prayer, with precaution and ablution for each prayer after its time has begun. If you abandoned prayer thinking it was menstruation, you must make up those prayers.