Is it obligatory to make up for the days of fasting in Ramadan during which blood was discharged? Is it permissible for a husband to have intercourse with his wife while she is experiencing intermittent bleeding? Is it possible to begin fasting the six days of Shawwal and the make-up fasts while still experiencing drops of blood?

You are experiencing Istihada (prolonged vaginal bleeding outside of menstruation). You must refer to your previous menstrual cycle and consider it as hayd (menstruation). If you do not have a previous cycle, then act according to the discerning blood (i.e., if the blood has characteristics of menstrual blood). If you cannot discern, then observe six or seven days as hayd, and the rest as istihada. When the days of hayd are over, you should perform ghusl (definition) (ritual bath), fast, and pray. You have all the rulings of pure women during the period of istihada, except that you must perform wudu (ablution) for each prayer after its time has begun.

Therefore, you are not required to make up the days you fasted in Ramadan (definition) except for the days considered hayd. You are permitted to fast the six days of Shawwal and other voluntary fasts during the days considered istihada. Your husband is also permitted to have intercourse with you during that period, as a woman experiencing istihada has all the rulings of pure women.