Is a woman considered pure and able to perform Hajj, Umrah, and prayer if bleeding stops ten days after childbirth, but a very light yellowish discharge continues, knowing that she usually does not see the sign of purity after menstruation and has started taking birth control pills?

The issue of yellowish and brownish discharge during the forty-day post-childbirth period is a matter of scholarly disagreement. Some scholars consider it part of nifas (postpartum bleeding), while others do not. As for anything beyond forty days, if it coincides with your regular menstrual cycle, then it is menstruation. If it does not coincide with it, then it is not menstruation, because the maximum duration of nifas, according to the preponderant opinion, is forty days. In this case, you would be considered to have istihada (non-menstrual bleeding), and you would be subject to all the rulings applicable to ritually pure women, and it is permissible for you to perform Hajj and Umrah.