The end of the period (becoming pure) may be known by one of two signs:
(1) Cessation of bleeding, and dryness in the place, so that if a woman inserts a piece of cloth etc, it comes away clean with no trace of blood or yellowish or brownish discharge.
(2) Emission of the white discharge, but some women do not get this discharge.
What you have mentioned about your period usually being six or seven days, and that you become dry after that, is sufficient to rule that you have become pure from menses, and you do not have to wait for the white discharge.
Al-Nawawi (may Allaah have mercy on him) said: The sign that the menses has ended and the woman has become pure is when the bleeding and yellowish and brownish discharge stop. When that stops the woman becomes pure even if some white discharge comes out after that or not. End quote from al-Majmoo’ (2/562).
If your period comes for two or three or four days, then it stops and the place becomes completely dry, ten you have become pure and you have to fast and pray, and you should not wait for the white discharge.
But if the place is not dry, rather there is some yellowish or brownish discharge, then you should not be hasty; and wait until it becomes completely clean or the white discharge comes. Women used to send pieces of cotton with traces of yellow to ‘Aa’ishah (may Allaah be pleased with her), and she would say to them: Do not hasten until you see the white discharge, meaning purification from menses. Narrated by al-Bukhaari in a mu’allaq report.
What you mention about the brownish threads is not regarded as menses if it appears before or after the usual period. But if it happens in connection with the bleeding, then it is regarded as menses, because of the hadeeth of Umm ‘Atiyyah (may Allaah be pleased with her) who said: We used not to regard brownish or yellowish discharge after purification (the end of menses) as anything that mattered. Narrated by al-Bukhaari (326) and Abu Dawood (307).
No differentiation is made between prayer and fasting with regard to a woman who is menstruating. Hence the Prophet (peace and blessings of Allaah be upon him) said of women: “Is it not the case that when she is menstruating she does not pray or fast?” Narrated by al-Bukhaari and Muslim.
It is haraam for a menstruating woman to pray and fast, and she has to make up the missed fasts but not the missed prayers. If these brownish threads came after the period ended, they are not of any significance and they do not mean that you should not pray and fast. But if they came before the tuhr (purification, end of the period) then they count as menses and it is haraam for you to pray and fast.
And Allaah knows best.