Does a brownish or yellowish discharge after seeing the sign of purity invalidate the fast of Ramadan 16, and is the fast of Ramadan 1, 2, and 6 valid, or must it be made up, bearing in mind the mentioned circumstances of seeing blood, its cessation, and taking birth control pills?

The blood that returns after forty days is considered nifas (post-natal bleeding) by the Shafi‘is and Malikis, and menstruation by those who do not stipulate the recurrence of the habit (for those who consider the maximum period of nifas to be forty days), and this is a strong opinion. As for the Hanbalis, they consider it istihadah (irregular bleeding) except for what coincides with the period of one's habit.

If it is considered nifas or menstruation, then the days during which the questioner saw blood must be made up. However, the yellowish and brownish discharge after the cessation of blood is not considered menstruation.