Must I perform my religious duties, take a ritual bath, and repeat the prayers I performed in the past few days, given that I use birth control pills and have brown discharge most days of the month, and my menstrual period only came in the first month of using them?

Yellowish and brownish discharges are considered menstruation if they occur during the usual period, or if they are connected to blood. Otherwise, they are not considered menstruation.

If you see brownish discharge during your usual period, perform ghusl (definition) (ritual bath) when you see purity. Otherwise, wait until your usual period ends, then perform ghusl and pray.

Anything beyond the usual period is considered istihadah (definition) (non-menstrual vaginal bleeding). In this case, perform wudu (ablution) for each prayer after its time has begun, while taking precautions by tying a cloth. Pray your fard (obligatory) and nawafil (supererogatory) prayers with that wudu until the time of the prayer expires.