Do the drops of blood that appeared before the completion of birth control pills count as istihadah (non-menstrual bleeding), which permits prayer, fasting, and reading the Quran, or as menstruation, which requires making up missed acts of worship?

Using birth control pills is permissible if it entails a benefit. The blood that appears fifteen days after the cessation of the last menstrual period is considered menses. The fasts of the days observed with it must be made up, but there is no need to make up the prayers. If the bleeding continues for longer than the usual duration, it is still menses; one must refrain from fasting and prayer, and everything forbidden to a menstruating woman remains forbidden. If the bleeding exceeds fifteen days, it is considered irregular bleeding (istihada). In this case, you should distinguish between menstrual blood and other blood: if it can be distinguished, then those days are menses and the rest is istihada. If it cannot be distinguished, then you should refer to your usual cycle: the days of your usual period are menses, and the rest is istihada. A woman experiencing istihada is treated as ritually pure.