What must a young man do about his practice of masturbation during the daytime in Ramadan when he was young and does not know the number of days he did it, nor if he was an adult?

As long as you were not certain of being an adult (baligh) while practicing that bad habit, you are not required to make up anything. If it is proven that you were an adult (baligh) while doing it, and you were ignorant that it invalidates the fast, then the preponderant view, according to us, is to excuse by reason of ignorance in such cases.