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 nawafil (supererogatory) , because they will make up for any shortfall in the obligatory prayers.
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.