Can women gather in the house of one of their number to offer Taraweeh prayer?

Firstly: 

It is permissible for women to gather to pray Taraweeh in the house of one of them, subject to the condition that there is no wanton display of adornments (tabarruj) involved in their going out, and that there is no danger of fitnah. 

Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) said: 

There is nothing wrong with women attending Taraweeh prayers so long as there is no danger of fitnah, subject to the condition that they go out in a decorous manner, not making a wanton display of their adornments or wearing perfume. End quote. 

Majmoo’ Fataawa Ibn ‘Uthaymeen, 14, question no. 808. 

But it is better for each of them to pray on her own in her house, and in an inner part of the house. The Prophet (peace and blessings of Allaah be upon him) said that it is better for women to offer obligatory prayers in their houses than to pray in the mosque, so it is more apt that this should also apply to naafil prayers. 

It was narrated from Umm Salamah (may Allaah be pleased with her) that the Prophet (peace and blessings of Allaah be upon him) said: “The best mosques for women are the innermost parts of their houses.” Narrated by Ahmad, 26002; classed as hasan by al-Albaani in Saheeh al-Targheeb, 341. 

Indeed it is better for a woman to pray in her home than to pray in congregation in al-Masjid al-Haraam (in Makkah) or in the Prophet’s Mosque behind the Prophet himself (peace and blessings of Allaah be upon him). 

It was narrated from Umm Humayd, the wife of Abu Humayd al-Saa’idi (may Allaah be pleased with them both) 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 your praying in your room is better for you than your praying in your house, and your praying in your house is better for you than your praying in your courtyard, and your praying in your courtyard is better for you than your praying in the mosque of your people, and your praying in the mosque of your people is better for you than your praying in my mosque.” So she gave orders that a ‘mosque’ be built for her in the innermost and darkest part of her house, and she used to pray there until she met Allaah (i.e., died). 

Narrated by Ahmad, 26550; classed as saheeh by Ibn Khuzaymah, 1689; classed as hasan by al-Albaani in Saheeh al-Targheeb, 340. 

Imam Ibn Khuzaymah included this hadeeth in a chapter entitled: It is preferable for a woman to pray in her house rather than in her courtyard, and in the mosque of her people rather than in the Mosque of the Prophet (peace and blessings of Allaah be upon him), even though one prayer offered in the Mosque of the Prophet (peace and blessings of Allaah be upon him) is equivalent to one thousand prayers offered in any other mosque. This is the evidence that the words of the Prophet (peace and blessings of Allaah be upon him), “One prayer in this mosque of mine is better than a thousand prayers in any other mosque” refer only to men and not women.  

Al-Shaykh ‘Abd al-‘Azeem Abaadi (may Allaah have mercy on him)said: 

It is better for women to pray in their houses because then there is no danger of fitnah. This ruling is even more emphatic because of the wanton display (tabarruj) and adornment of women.  

‘Awn al-Ma’bood, 2/193 

Secondly: 

If women gather together in one house in accordance with the conditions mentioned above, it is permissible for them to pray in congregation. The one who is leading them in prayer should stand in the middle of the (first) row, not out in front, and she should not lead men in prayer even if they are her mahrams. She should recite our loud just as men do in the prayers where reciting out loud is required, so long as no men except her mahrams can hear her voice. 

It was narrated that Umm Waraqah bint ‘Abd-Allaah ibn Nawfal al-Ansaariyyah asked the Prophet (peace and blessings of Allaah be upon him) for permission to appoint a muezzin in her house who would call her to prayer, and he told her to lead the people of her household in prayer. 

Narrated by Abu Dawood, 591; classed as hasan by Shaykh al-Albaani in Irwa’ al-Ghaleel, 493. 

And it was narrated from ‘Aa’ishah that she would give the call to prayer and lead other women in prayer, standing in the middle of the row. 

And ‘Aa’ishah led women in obligatory prayers, standing in the midst of them. 

And it was narrated that Hujayrah bint Haseen said: Umm Salamaah led us in prayer standing in the midst of the women. 

And it was narrated from Umm al-Hasan that she saw Umm Salamah, the wife of the Prophet (peace and blessings of Allaah be upon him), leading women in prayer, standing with them in their row. 

Shaykh al-Albaani (may Allaah have mercy on him) said, after narrating these reports: 

In conclusion, these reports are sound and may be acted upon, especially since they confirm the general meaning of the words of the Prophet (peace and blessings of Allaah be upon him): “Women are the twin halves of men…” 

Sifat Salaat al-Nabi (peace and blessings of Allaah be upon him), p. 153-155. 

Ibn Qudaamah (may Allaah have mercy on him) said: 

She should recite out loud in prayers where it is required to recite out loud, but if there are any men present, she should not recite out loud, unless they are her mahrams, in which case she may do so. 

Al-Mughni, 2/17 

And Allaah knows best.