Was her fasting valid if she was fasting on Mondays and Thursdays with the intention of making up missed days if she owed any, and with the intention of a supererogatory fast if she did not owe any, given that she does not know the number of days she missed, and must she fast again or offer expiation if her fasting was not valid?

If one intends to observe a voluntary fast, such as on Mondays and Thursdays, with a hesitant intention—meaning they intend it as a compensatory fast if they have make-up days due, and as a supererogatory fast if they do not—then their fast is valid and suffices as make-up if they have any. However, this should not be adopted as a permanent practice. Rather, she should ascertain the days for which she is uncertain about making up, and strive to clear her conscience with a firm intention, either as a compensatory fast or a supererogatory one, to avoid doubts and whispers (waswas) in worship.