How can the beginning and end of menstruation be determined for prayer and fasting when intermittent spotting (in the form of scattered drops) is caused by the use of a birth control device?

If the drops and bloody discharges continue for a full day and night, or if their total duration reaches that much within fifteen days, then it is menstruation (hayd). In this case, you must refrain from what a menstruating woman refrains from, and make up any missed obligatory fasts. If the blood duration exceeds fifteen days in a month, then anything beyond that is irregular bleeding (istihada). If you can distinguish menstrual blood, then that is menstruation, and anything else is istihada, for which the rulings of a pure woman apply, except for performing ablution (wudu) for each prayer. If you cannot distinguish, then refer to your previous menstrual habit, and anything exceeding it after fifteen days from the start of the bleeding is istihada. However, if the drops and discharges do not continue for a full day and night, and their total duration does not reach that much within fifteen days, then it is dysfunctional bleeding (dam fasad), and you are obligated to pray and fast during it.