Brownish discharge one day after menses ended
Question

My period began one day, then after that it stopped and I had a brown discharge. Then after that it came again (I mean my period is four days), then after one day there was nothing. I did ghusl and went to pray Taraweeh, and I prayed and read Quran and fasted. Then the period came again at night. Do I have to make up that day? And the Quran that I read, do I have to read it again?.
Praise be to Allah.The end of the period (tuhr) may be known from one of two signs: emission of the white discharge, which is known to women, or complete dryness, such that if one places a piece of cotton and the like on the site, it comes away clean with no trace of blood or yellow on it. 
The menstruating woman may see blood for one or two days or more, then she may become pure for a day or more, then bleed again. 
If the brownish discharge or spots appear after she has become pure (tuhr), then it is not regarded as menses. If that appears before she has become pure, then it is part of the period. 
Based on that, we say: 
1 – The ceasing of bleeding after the first day: if what is meant is that it was completely dry, then in the case you should do ghusl and pray and fast, because you have become pure. If it did not become completely dry, then it is still menses, and the brownish discharge that appeared after that is regarded as part of the period. 
2 – If the bleeding stopped after four days and you saw the white discharge or it was completely dry, then you did right by doing ghusl and starting to pray and fast. If the bleeding resumed at night, then it is menses, but it does not affect your prayers and fasting on that day, so the prayers are valid and the fast is valid.  
3 – With regard to reading Quran, it is permissible for a menstruating woman. This has been discussed in the answer to question no. 2564. What is not allowed for a menstruating woman is touching the Mus-haf, so if she wants to read Quran she should wear gloves or turn the pages of the Mus-haf with a handkerchief so that she will not be touching the Mus-haf directly. 
Whatever the case, you do not have to read again what you had read of Quran, and you will have the reward for that in sha Allah. 
And Allah knows best.