When fasting became obligatory for me, I did not fast my first Ramadan, because I did not know and I was unaware that it was obligatory for me. But then I realised that it was obligatory for me. That was in the last week of Ramadan, but I had my menses, then I became pure there were four days left of Ramadan, and I did not fast them, because I was sick and I was vomiting. Do I have to fast an entire month, or offer a fidyah? But I do not remember exactly how many days I did not fast. Also, I did not pray during the year in which it became obligatory for me to fast, because I did not know at that time. Should I make up these prayers also?

Praise
be to Allah

You have to make
up whatever you did not do of the Ramadan fast, whether that was the days of
your period or the rest of the month. If you do not know how many days you
owe, then you should do your best to work it out, and fast as many days as
you think most likely will fulfil what you owe.

Shaykh Ibn
‘Uthaymeen (may Allah have mercy on him) said:

If a person did
not fast out of ignorance, thinking that fasting was not obligatory for him,
such as if a woman reaches puberty by beginning to menstruate when she is
young, and she does not think that puberty is reached except by reaching the
age of fifteen years, then she has to make up Ramadan, because obligatory
duties are not waived on the basis of ignorance.

This issue
happens a great deal to some women who begin their periods when they are
young, and they are too shy to tell their families that they are
menstruating, so they do not fast, or sometimes they fast even on the days
of their menses.

We say to the
one who did not fast: You must make up the months in which you did not fast
after you reached puberty.

And we say to
the one who used to fast during the days of their menses: You have to repeat
the days that you fasted during your menses, because fasting during menses
is not valid.

End quote from
Fataawa Noor ‘ala ad-Darb by al-‘Uthaymeen (2/11)

With regard to
prayer, you should offer a great deal of naafil (supererogatory) fasts,
because they will make up for any shortfall in the obligatory fasts.

At-Tirmidhi
(413) narrated that Abu Hurayrah said: I heard the Messenger of Allah
(blessings and peace of Allah be upon him) say: “The first deed for which a
person will be brought to account on the Day of Resurrection is his prayer.
If it is sound then he will prosper and succeed, but if it is not sound,
then he will fail and lose. If his obligatory prayer is lacking, the Lord,
may He be glorified and exalted, will say: Look and see whether My slave has
any voluntary prayers to make up for what is lacking of his obligatory
prayer. Then the rest of his deeds will be examined in like manner.”

Classed as
saheeh by al-Albaani in Saheeh at-Tirmidhi.

And Allah knows
best.