Is it permissible to make up missed prayers (qada'), and does abundant performance of supererogatory prayers (nawafil) compensate for them, especially given uncertainty about ritual purity from menstruation?

If there is doubt about the cessation of menstruation, then it is not obligatory to make up the prayers, because certainty is not removed by doubt. However, if purity is certain, then ghusl (ritual bath) is obligatory, and the prayers whose time was reached while in a state of purity must be made up. Increasing voluntary prayers (nawafil) is recommended, and it compensates for deficiencies in obligatory prayers, due to the Prophet's (peace be upon him) saying: "Help me against yourself by prostrating much," and due to His (Allah's) saying in the Hadith Qudsi: "Look, does My servant have any voluntary prayers? If he has voluntary prayers, He says: Complete for My servant his obligatory prayer from his voluntary prayer." Therefore, increase your voluntary prayers and abandon obsessive doubts, for doubt does not remove certainty.