Must I make up the prayers and fasting that I missed in the past, based on my mistaken belief that the age of legal majority (baligh) is only menstruation, and that I did not intend to fast during the night with a firm intention?

The question is incomplete. In any case, if you reached puberty through a sign other than menstruation, and then missed some prayers or days of Ramadan, thinking that you had not reached puberty, then count what you missed of the obligatory prayers and fasting and make them up. Making them up is obligatory according to the majority of scholars, unlike Shaykh al-Islam Ibn Taymiyyah.