Should I fast with the intention of making up (for missed fasts) or as a supererogatory fast, or should I break my fast to take medicine, if I slept before forming the intention overnight for an obligatory make-up fast? And is it permissible to follow the doctor's advice regarding taking medicine, and what are the implications of that for not making up the fast?

It is not valid to fast this day as a makeup for Ramadan, due to the lack of a firm intention from the night before dawn, as the Prophet, peace and blessings be upon him, said: "Whoever does not intend to fast before dawn, there is no fast for him." However, if you complete the day as a supererogatory (nafl) fast, that is permissible, because the intention for a supererogatory fast is not required from the night. And if you break your fast this day, there is no harm, especially if you need the medicine.