What is incumbent upon a woman who broke her fast on a number of days in Ramadan when she was young, then another Ramadan came upon her before she made up those days, and she does not remember the number of days or whether she was obligated to make up the fast and feed the poor except after she has grown older? And what should she feed the poor if feeding them is obligatory?

You must make up for the fasting days you missed after puberty, even if you were unaware of the obligation to make them up. You should make up what you believe, with high probability, will clear your conscience. Ignorance removes the sin but not the obligation. The basic rule is that expiation (kaffarah) is obligatory for whoever delays making up missed fasts until the next Ramadan without a valid excuse, which is feeding one poor person for each day. However, no ransom (fidyah) is due from you because of your ignorance of the prohibition of delaying the make-up. Al-Adhra'i said: "If he delayed it due to forgetfulness or ignorance, then there is no fidyah."