She is not sure whether her prayer and fasting are valid
Question

                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 Allah.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.