What is the ruling regarding the days I broke my fast in Ramadan, and is expiation (kaffarah) obligatory upon me, given that I stopped fasting and praying due to a discharge (al-kadrah) which I could not discern whether it was menstruation (hayd) or abnormal bleeding (istihadah)? And what should I do concerning fasting the six days of Shawwal and fasting to make up for Ramadan (qada' Ramadan)?

You did well in making up your prayers and fasts. What descended upon you at the end of Ramadan and Shawwal is not menses, but rather a brownish discharge that neither precedes nor follows menses. Therefore, you must make up the fasts of the first, second, and third days. This brownish discharge and secretions are not istihadah (prolonged non-menstrual bleeding). However, if it persists, you would be subject to the rulings of a woman with istihadah: you would perform ablution for the time of each prayer, and whatever exits would not harm you.