She is not sure whether her prayer and fasting are valid

I feel ashamed to ask this question because of the abhorrence of what I used to do, and I do not even like to mention it.
 A few years ago I used to do two horrible things. The first is that a female relative and I used to fondle one another and we continued to do that for a while, then we stopped. The second is that I used to mistreat the young son of our neighbours; I used to hit him time after time and make him kiss me or touch part of my body. I do not even like to mention these things because it makes me feel that I am bad. I really regret having done these things.  I have a number of questions.
1- Do I have to fast the days on which I did those things, although I did not know that they invalidate my fasting and prayers?
2- Do I also have to repeat the prayers?
3- I do not know if any fluid was emitted or not.
4- I am confused and uncertain, and I do not remember if I did those things in Ramadaan or not?
5- If I have to fast, how can I work out the number of days? I tried hard to work it out but I do not remember exactly when I did those things.
6- When does a girl become accountable for her fasting? Is it after she reaches puberty? I mean, is it after she gets her monthly period for the first time?.

Praise be to Allaah.
Firstly:

We praise Allaah for having enabled you to repent from these haraam deeds, and we ask Allaah to accept your repentance.

Secondly:

You do not have to make up any of the prayers or fasts, for the following reasons:

1-     You did not know that this would invalidate your fasting and prayers. If a person does something haraam without knowing that it is forbidden, then he may be excused and does not deserve to be punished for this sin. Allaah says (interpretation of the meaning): “And there is no sin on you concerning that in which you made a mistake, except in regard to what your hearts deliberately intend. And Allaah is Ever Oft‑Forgiving, Most Merciful” [al-Ahzaab 33:5]. Ignorance is a kind of mistake, because the one who is unaware does not deliberately commit sin. See the answers to questions no. 50017 and 45648.

2-     You are not certain that any fluid was emitted. If a Muslim does an act of worship, the basic principle is that it is judged to be valid, so long as he is not certain that it was not valid. Merely doubting does not invalidate an act of worship once it has been done.

Thirdly:

With regard to a girl becoming accountable for fasting and other Islamic rulings, that happens when she reaches puberty, and a girl reaches puberty when one of four signs occur:

1-     Reaching the age of fifteen

2-     Growth of coarse hair around the private part

3-     Emission of maniy (fluid emitted at climax)

4-     Menstruation.

It is not essential that all of these happen at once, rather one sign is sufficient to establish that puberty has been reached.

See also the answer to question no. 21246.

We ask Allaah to enable you to do all that is good. And Allaah knows best.