It is permissible for a woman to go out and pray in the mosque with the congregation, whether that is an obligatory prayer or Taraaweeh, but praying in her house is better for her.
Ahmad (27135) narrated from Umm Humayd, the wife of Abu Humayd al-Saa’idi, that she came to the Prophet (peace and blessings of Allaah be upon him) and said: "O Messenger of Allaah, I love to pray with you." He said: "I know that you love to pray with me, but praying in your house is better for you than praying in your courtyard, and praying in your courtyard is better for you than praying in the mosque of your people, and praying in the mosque of your people is better for you than praying in my mosque."
Classed as hasan by al-Albaani in Saheeh al-Targheeb wa’l-Tarheeb and by Shu’ayb al-Arna’oot in Tahqeeq al-Musnad.
If a woman prays in the mosque, it is better for her to be far away from the men, hence the back rows for woman are preferable to the front rows, because they are further away from the men. When the Prophet (peace and blessings of Allaah be upon him) said salaam at the end of the prayer, he would stay where he was for a little while and would not move, to let the women leave so that the men would not mix with them.
Muslim (440) narrated that Abu Hurayrah said: The Messenger of Allaah (S) (peace and blessings of Allaah be upon him) said: “The best rows for men are at the front and the worst are at the back; and the best rows for women are at the back and the worst are at the front.”
There is nothing wrong with a woman praying in a place where men can see her, such as al-Masjid al-Haraam (in Makkah) or the courtyard of the mosque, or wherever she needs to pray in the countryside and so on, so long as she covers all of her body, even her face and hands, according to the more correct view. That is because women are enjoined to cover their faces and hands in front of non-mahram men. The evidence for that is discussed in the answer to question no. 11774 and 21536.
The scholars of the Standing Committee for Issuing Fatwas were asked:
Question: How should a woman pray if there are non-mahram men with her, for example in al-Masjid al-Haraam, and when travelling if there is no mosque on the road where women can pray?
A woman is required to cover all of her body when praying, except the face and hands, but if she is praying where there are non-mahram men who can see her, then she has to cover all of her body including the face and hands. End quote.
Fataawa al-Lajnah al-Daa’imah (7/339).
And Allaah knows best.