What is the ruling on one who did not fast Ramadan upon reaching puberty, due to his family's belief that he was not yet obligated, and what is incumbent upon him if he does not know when he reached puberty, and what is the ruling on one who broke his fast believing that the time had begun upon hearing "Hayya 'ala al-Salah" from the Adhan?

Whoever did not fast after reaching puberty must make up the days they missed. If one is unsure about the exact time of puberty, the default assumption is that it occurred at a later age, and they are only required to make up what they are certain became obligatory upon them. If puberty was marked by a wet dream (احتلام), then the matter is clear. If they did not experience a wet dream and acted according to the opinion of those who consider puberty to be at eighteen years of age, then there is nothing against them, especially if this is the prevalent opinion in their country. As for doubt concerning the validity of an act of worship after completing it, it does not affect its validity.