How can a young man who has not been regular in prayers and fasting since puberty make up for the missed ones, especially since he does not remember the reasons for breaking his fast?

Expiation (kaffarah) for intentionally breaking the fast is not obligatory except through sexual intercourse, according to the preponderant opinion. You are required to make up the days you missed fasting. You are also required to calculate and make up the missed prayers and fasting days from the time of puberty until repentance. If you are unable to ascertain the exact number, then act based on your best estimation (taharri) and make up what you believe will absolve your responsibility. You are not required to pay expiation for delaying the make-up fasts as long as you were ignorant of the ruling.