Opinions on women passing between a person praying and his/her sutra: Hadith that state that a person's prayer will be invalidated by the passing in front by a woman, a dog or a donkey.
"Salaah is invalidated by (the passing of) a black dog or a menstruating woman, (i.e. a woman who has reached puberty)." [Ahmad and Aboo Daawood]
"Salaah is repeated due to the passing of a donkey, a woman or a black dog". [Ibn Khuzaymah]
It was reported by Abdullah Ibn Samit that Abu Dhar said that the Messenger of Allah said: "If any of you wish to perform Salaat, he is indeed shielded if he has in-front-of him something the size of the rear end of a camel's saddle. If there isn't something, the size of the rear a camel's saddle in-front-of him however, then (the passing of) a donkey, a woman or a black dog can invalidate his Salaat." I said: Oh Abu Dhar! What is it with a black dog as opposed to a red or yellow dog?!" He said: "Oh my son of my brother! I asked the Messenger of Allah just as you have asked me, and he said: "A black dog is Shaytan." [Saheeh Muslim].
Abu Hurayrah, Anas, Ibn 'Abbaas, Al-Hassan Al-Basri, and some from the Shafi' school of thought (those after Shafi' as Shafi' himself was of the opinion that women, dogs, or donkeys passing a person praying does not invalidate one's prayer, rather that the blessings are decreased) are all of this opinion that if a woman, a dog, or a donkey passes in between a person and his/her sutra whilst they are praying, that they have then invalidated that person's prayer (Tamamul Minnah p. 300). The Hanbali school of thought and 'Aisha were of the opinion that only a black dog passing in between someone praying and their sutra will invalidate their prayer. The Hanafi school of thought does not consider a prayer invalidating by the passing of a woman, a dog, or a donkey between the person praying and his/her sutra (Al Mabsut Vol. 1, page 191).
Opinions are divided when it comes to whether the person's prayer is invalidated when a female passes in front of a person praying. Opinion is further divided as to whether the invalidation occurs dependent on what age the female is, some say 7 years of age and others say once the female hits adulthood (adulthood being considered as soon as she has her first period). Opinion is also divided as to whether only the prayers of a male is invalidated by the passing female, or whether it is both the male and female who's prayers are invalidated by the passing female.
Ibn Hazm is of the view that if a woman passes in front of a praying man she invalidates his prayer, but does not invalidate the prayer of a female if she passes between her and her sutra. He said:
"A woman passing in front of another praying woman does not invalidate her prayer."
According Al-Albani who has been said to be hanbali scholar and of the salafi movement, has said in answer to a question that a woman who passes between a praying person and their sutra irregardless of the praying person's gender, invalidates the praying person's prayer.
A woman invalidating a woman’s prayer
source: silsilat ul-hudā wa nnūr ~ the series of guidance and light ~ tape no. 93
Question #7: “The woman who has reached puberty invalidates the prayer by her passing in front of the one praying, so does she invalidate the prayer of a woman?”
Shaykh al-Albānī answers:
“Yes, the woman invalidates the prayer of another woman (if she passes in front of her), with the condition mentioned in some established narrations: if she has reached puberty. And there is no difference in Islamically legislated rulings between men and women, except that which came in text excluding women from the men; and there is no (such) text here. Rather the text is general: the woman (who has reached puberty), the donkey and the black dog invalidate the prayer of one of you when they pass in front of him, if there isn’t something like the rear part of a camel saddle in front of him.1 So there is no difference in the ruling.”
Opinion on women leading men in prayer or praying next to a man: By in large the majourity of 'ulema and the Four Schools of Thought (Hanafi, Maliki, Shafi', and Hanbali) have forbidden women from leading men in prayer.
Yusuf Tawfiq Choudry who is from the Hanbali madhab says that women may not lead men in prayer:
The scholars of Islam have complete consensus on the fact that it is not permissible for women to lead a man in an obligatory prayer. Ibn Hazm [d. 456A.H.] rahimahullah says:
"They [the scholars] have agreed that a woman is not permitted to lead a man in [obligatory] prayer. If they were to do that [i.e. a woman led a man in obligatory prayer], then their prayers are invalidated by complete consensus." [Maratibul-Ijma, Ibn Hazm, p27, Darul-kutub al-Ilmiyyah]
Imam Ibn Hubierah [d. 560A.H.] says:
"They [the scholars] have complete consensus that it is not permissible for a woman to lead a man in prayer in obligatory prayers." [Al-Ifsah, Al-wazir Ibn Hubirah, vol. 2, pg 42, Markaz al-Fajr]
Ibn Masud said as reported by Abdur-Razzaq in his Musannaf and authenticated by Ibn Hajr: "The men and women in the time of the Children of Israel used to pray together and the women used to lead the men in prayer. So Allah caused them to have menstruation and so stopped them from the mosques." As for the narration from Aishah, then it states: "The women of the Children of Israel used to take wooden shoes and to be distinguished and lead the men in the masjids, so Allah prohibited the masjids upon them [the women] and punished them with menstruation."
http://www.islaam.net/main/display_article_printview.php?id=1384A Woman's Prayer Beside a Man: A group of Imami legists observe: If
a man and a woman perform salat in a single place so that she is either
in front of him or beside him, and there is neither any screen between
them nor does the distance between the two exceed 10 cubits, the
salat of the one who starts earlier will not be invalid, and if both start
simultaneously, the salat of both will be invalid.
The Hanafis say: If the woman is in front or beside a man, the
salat will be invalid if performed in a single place with no screen at least
a cubit high between them, the woman has sex appeal, her shanks and
ankles are adjacent to his, the salat is not a funeral prayer, and the
salat is being jointly performed, i.e. either she is following him or both
are following a single imam.
The Shafi'is, the Hanbalis and most Imamis are of the view that the salat is valid, though the manner of performance is makruh.
(Prayer (Salat), According to Five Islamic Schools of Law: (Part III) By: 'Allamah Muhammad Jawad Maghniyyah)
The Maliki school of thought considers the prayer of a male invalid if he prays next to a woman (without a barrier) or behind a woman.
http://www.aswjonline.com/prayerpurification.htm Ibn Majah, narrated through Jabir ibn Abdullah: "A woman may not lead a man in Prayer, nor may a Bedouin lead a believer of the Muhajirun or a corrupt person lead a committed Muslim in Prayer." (Sunan Ibn Majah)
Imam an-Nawawi, “If a woman leads a man or men in a congregational prayer, the prayer of the men is invalid. As for her prayer, and the prayer of the women praying with her, it is sound.”
“Behold! A woman is not permitted to perform the Imamat of men” (Sunan Ibn Maja: Book of establishing Prayer: Hadīth no. 1081)
However, there are a minority of 'ulema who have stated that it is permissible for a woman to lead a man in prayer, and most of those from the minority who have said this is permissible, have stated that it is only for nawafil salaat in the home and only if the woman is more knowledgeable than the men (knows more Qu'ran), and the general agreement amongst them is that a woman must stand behind the men to lead them in prayer based on their interpretation the hadith of Umm Waraqa***. Such 'ulema who've stated that it is permissible for women to lead men in prayer at home for the nawafil, are Imams Abi Thaur, al-Muzani, and Ibn Jarir.
http://www.altmuslimah.com/a/b/a/leading_scholar_hamza_yusuf_on_women_leading_prayer/ *** 'Ulema who say it is forbidden for women to lead men in salaat also quote Umm Waraqa's hadith saying that it shows that women are only permitted to lead other women in prayer, not men.
Regarding women leading women in prayer and women's position in congregation: Al-Haafiz said in al-Fath: This hadeeth teaches us a number of things… that women should stand behind the men’s rows, and a woman should form a row on her own if no other woman is present.
The Maliki school of thought considers the prayer of anyone male or female to be invalid if he/she prays next to a woman (without a barrier) or behind a woman.
http://www.aswjonline.com/prayerpurification.htm and also [Bulghatus Salik vl.1, pg.146; Ashalul Madarik, vl.1,pg.241]
According to the Hanafi school of thought a woman may lead other women in salaat and their prayers are valid, however it is considered makrooh tahriman (Maraqi al-Falah, Hashiyat Ibn Abidin).
Imam Muhammad ibn Al Hasan Al Shaybäni [d.189] writes, “We are not pleased by women leading the prayer however if they do so they should stand in the middle of the row among women just as `Ä’isha رضى الله عنها did. This is the view of Imam Abu Hanëfa.” [Kitäb Al Aathär p. 57, Maktaba Imdadiya, Multan, Pakistan]
The Shafi School of Thought and most jurists from Hanbali school of thought also allowed women to lead other women in prayer and is considered mustahab for women to lead other women (not men) in prayer at home if there is no qualified male available. [Ahkaam al-Imaamah wa’l-I’timaam by al-Muneef, p. 319-320]
`Atä reported that `Ä’isha would call the adhän and iqäma and would lead women in prayer and (while doing so) she would stand in the middle of them’. [Mustadrak: 731 & Sunan Al Bayhaqe: 5356]
`Ammär Al Duhani reported that a woman from his tribe named Hajëra said, “Umm Salama led them (i.e. the women) in prayer and stood in the middle (of the row).” [Sunan Al Bayhaqë: 5357]