What is the ruling of the Shari'ah regarding making up for missed fasting and prayers, and estimating the number of days when the time of committing prohibitions is not remembered? And is a girl held accountable for her fasting after puberty or after her first menstruation?

You are not required to make up for the prayers and fasting because you were unaware that those actions invalidate fasting and prayer. An ignorant person is excused and not punished for a sin. Furthermore, you are not certain that anything was discharged from you, and the default assumption is the validity of worship unless its invalidity is certain. As for a girl being obligated to fast and other duties, this is established by puberty. Its signs are: reaching fifteen years of age, or the growth of coarse hair around the private parts, or the discharge of semen, or the onset of menstruation. The realization of just one sign is sufficient.