Do the mentioned acts (forcefully pouring water into the vagina and the subsequent feeling and discharge) count as masturbation necessitating ghusl and invalidating prayer and fasting, and is it obligatory to make up prayers and fasts from the age of puberty, given the inability to ascertain the number and days, and was touching the Mus’haf in that state haram?

Masturbation is forbidden, and you must repent from it. Your fasting on the days you committed this act during Ramadan was valid due to your ignorance that it nullifies the fast.

As for the prayers: If you were certain that semen, which necessitates ghusl (ritual bath), was discharged and you did not perform ghusl, then you must make up those prayers according to the majority of scholars. Some scholars (like Ibn Taymiyyah) hold the view of exemption due to ignorance. If you wish to make them up but do not know the number, then make up what will give you certainty or a strong presumption that you have fulfilled your obligation.

However, if you were not certain that what was discharged from you was semen, then your prayers are valid, and you are not required to make them up. Whoever doubts whether what was discharged from him is semen or madhi (pre-seminal fluid) may choose [to consider it either].