Are Women Permitted to Pray in front of Non-Mahrams?
Question

During Ramadan the Masajid here becomes full, Alhamdulillah. So they have to prepare additional places outside the Masjid. Some women may not be able to find a place within this additional place, which is nearly covered, so they pray outside. I used to return without performing the prayer if I find that there is no concealed place, and pray, instead, at home. Today I was discussing this matter with a sister who said to me that there is no evidence to prove that a woman cannot pray in a place where she might be seen by others. She added that as long as you go out and talk to the sellers and drivers, why can’t you pray in front of them as well. She said that women pray beside men in the Haram (Sacred Masjid). Unfortunately I did not have a Hadith as evidence to prove that she is wrong and I am right. I promised to bring her a detailed answer after searching, if Allah wills. Please clarify this matter to me, and tell me why women are allowed to pray beside men in the Haram.
Praise be to Allah.Can a woman go out and pray in the mosque?
It is permissible for a woman to go out and pray in the mosque with the congregation, whether that is an obligatory prayer or Tarawih, but praying in her house is better for her. 
Ahmad (27135) narrated from Umm Humayd (may Allah be pleased with her), the wife of Abu Humayd As-Sa`idi (may Allah be pleased with him), that she came to the Prophet (peace and blessings of Allah be upon him) and said: "O Messenger of Allah, 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 sound by Al-Albani in Sahih At-Targhib wat-Tarhib and by Shu`ayb Al-Arna’ut in Tahqiq Al-Musnad) 
Which rows are best for women in prayer? 
If a woman prays in the mosque, it is better for her to be far away from the men, hence the back rows for women are preferable to the front rows , because they are further away from the men. When the Prophet (peace and blessings of Allah be upon him) said Salam 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 (may Allah be pleased with him) said: The Messenger of Allah (peace and blessings of Allah 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.” 
Can a woman pray in front of non-Mahrams?
There is nothing wrong with a woman praying in a place where men can see her , such as Al-Masjid Al-Haram (in Makkah) or the courtyard of a 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 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-Haram, and when travelling if there is no mosque on the road where women can pray? 
They replied: 
“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.” (Fatawa Al-Lajnah Ad-Daimah (7/339)
And Allah knows best.