What is the ruling on the fasting and making up of a girl who did not inform her family of her puberty in Ramadan, and thought herself pure after three days of her period, with the presence of blood spotting?

You must repent to Allah Almighty for your negligence in learning the rulings of Sharia and for prioritizing shyness from people over shyness from Allah. You must make up all the days you did not fast due to menstruation, whether the first eight days or the blood spots that appeared later, because fasting during them is invalid. If you cannot calculate them precisely, then make up what you believe will absolve your responsibility. You also owe a fidyah (expiation) of feeding a poor person for each day whose make-up was delayed until after the following Ramadan, unless you were ignorant of the impermissibility of the delay. If you did not perform ghusl after the end of menstruation, contenting yourself with the first ghusl, then you must make up the prayers you performed during that period. The more cautious approach is to make them up, and this is the view of the majority of scholars.