She thought that she was in nifaas following a miscarriage so she did not fast or pray

Firstly: 

If a woman miscarries, the bleeding that follows is not
regarded as nifaas (post partum bleeding) unless the miscarried foetus had
developed human features such as a head, hand, foot and so on. 

The blood that she passes is not considered to be nifaas
unless the foetus had human features.  

Human features do not appear in the foetus before eighty days
of pregnancy, because the Prophet (peace and blessings of Allaah be upon
him) said: “The creation of any one of you is put together in his mother’s
womb for forty days, then he becomes a ‘alaqah (a piece of thick coagulated
blood) for a similar period, then he becomes like a chewed piece of flesh
for a similar period, then Allaah sends an angel who is enjoined to write
down four things, and it is said to him: ‘Write down his deeds, his
provision, his lifespan and whether he is doomed for Hell or destined for
Paradise. Then the soul is breathed into him.” Narrated by al-Bukhaari,
3208.  

This hadeeth indicates that a human being goes through a
number of stages during pregnancy.  

For forty days he is a nutfah (mixed drops of male and female
sexual discharge, for the next forty days he is a ‘alaqah (a piece of thick
coagulated blood), then for forty days he is a mudghah (a lump of chewed
flesh), then the soul is breathed into him after one hundred and twenty days
have passed.   

Human features begin to appear at the mudghah stage, not
before that, because Allaah says (interpretation of the meaning):  

“O mankind! If you are in doubt about the Resurrection,
then verily, We have created you (i.e. Adam) from dust, then from a Nutfah
(mixed drops of male and female sexual discharge, i.e. the offspring of
Adam), then from a clot (a piece of thick coagulated blood) then from a
little lump of flesh — some formed and some unformed (as in the case of
miscarriage) — that We may make (it) clear to you (i.e. to show you Our
Power and Ability to do what We will)”

[al-Hajj 22:5]  

From this verse it is known that the mudghah may or may not
have human features. 

Ibn Qudaamah (may Allaah have mercy on him) said: If a woman
sees blood after passing something in which there were human features, then
it is nifaas. This was stated by Imam Ahmad. But if she see that [bleeding]
after passing a nutfah or ‘alaqah, then it is not nifaas. End quote from
al-Mughni, 1/211. 

Shaykh ‘Abd al-‘Azeez ibn Baaz (may Allaah have mercy on him)
said: If a woman miscarries something in which human features are visible,
such as a head, hand, foot and so on, then she is in nifaas, and comes under
the rulings on nifaas, so she should not pray or fast and it is not
permissible for her husband to have intercourse with her until she becomes
pure or until forty days have passed.  

But if there are no discernible human features in that which
is passed by the woman, and it is like a piece of meat with no features, or
it is blood, then that comes under the rulings on istihaadah (non-menstrual
vaginal bleeding) and not the rulings on menstruation, and she has to pray
and fast in Ramadan, and she is permissible to her husband, because she
comes under the rulings on istihaadah according to the scholars. End quote
from Fataawa Islamiyyah, 1/243. 

Shaykh Ibn ‘Uthaymeen said:  

The scholars said: If something is passed in which human
features appear, then the blood which is passed after it emerges is regarded
as nifaas, during which the woman should not pray or fast and her husband
should avoid intimate relations with her until she becomes pure. But if what
is passed is not formed, then the bleeding is not regarded as nifaas, rather
it is irregular bleeding which does not prevent the woman from praying or
fasting or anything else. 

The scholars said: The minimum time in which human features
may appear is 81 days. 

Fataawa al-Mar’ah al-Islamiyyah,
1/304, 305 

Based on that, the bleeding which you experienced was not
nifaas, because the foetus was miscarried before the completion of 80 days,
and you should have prayed and fasted during that period, unless your menses
came to you. 

Secondly: 

You have to make up the fasts, and there is no confusion on
this issue, regardless of whether we say that you were pure or in nifaas,
because the one who does not fast for a reason (such as sickness or menses
or travelling) is obliged to make up the fast. You did not fast for a
reason, which is that you thought you were in nifaas. 

As for making up the prayers, it seems that you are not
obliged to make them up, because the Prophet (blessings and peace of Allah
be upon him) did not tell the woman who was suffering istihaadah and did not
pray during the time she was bleeding to make the prayers, rather he advised
her as to what she should do in the future. 

Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him)
said: If the woman who is suffering istihaadah did not pray for a while
because she believed that prayer was not obligatory for her, then there are
two opinions as to whether it is obligatory for her to make up the prayers
or not. The first view is that she does not have to make them up, as was
narrated from Maalik and others, because when the woman who was suffering
istihaadah said to the Prophet (blessings and peace of Allah be upon him):
“I experience severe and painful bleeding that prevents me from praying and
fasting,” he told her what she should do in the future but he did not tell
her to make up the past prayers. End quote from Majmoo’ al-Fataawa
(22/102). See also the answer to question number
45648. 

To sum up: 

You have to make up the fasts. As for the prayers, if it is
easy to you to make them up, then do that. Otherwise we hope that Allah will
pardon you for that. And we advise you to strive to seek knowledge and
understanding of your deen. 

We ask Allah to help and guide us and you. 

And Allah knows best.