1) On the face of it, It refers to the fact that no woman should arrange/officiate the Nikah of another woman by representing as her Wali (Guardian). This narration is categorized Sahih by Shiekh Albani Except for the word adulteress in it.
2) It needs to be understood that Nikah belongs to long held Sunnah of Prophets in Islam even before Prophet Muhammad (sws) and was instituted by Prophet Muhammad (sws) as well after his ratification. Marriage is an open declaration of a contract by a man and a woman to live permanently as husband and wife. It is declared in the presence of people through a responsible personality with great solemnity and gravity after he delivers a sermon to counsel and guide them. It is evident from divine scriptures that this way was adopted from the very birth of man on this earth. Consequently, the Quran was not required to give a new directive in this regard. As an age old sunnah of the prophets, Muhammad (sws) passed it on to his ummah thus keeping it intact. It should be kept in mind that it is essential for the sanctity of the institution of family – the very institution marriage creates – that marriage takes place with the consent and presence of the elders of the family. There is no doubt about the fact that the decision of marriage is primarily taken by the concerned man and woman. However, if the marriage does not take place through the consent of the guardians or the elders of a family, then there must be a solid reason for this. In the absence of such a reason, a state has the authority to stop such a marriage from taking place (This however does not mean that if a marriage has taken place without the consent of the parents, then it shall be declared illegal). Narratives such as لَا نِكَاحَ اِلَّا بِوَلِى (no marriage should take place without the [permission of] the guardian) and other similar ones actually allude to this aspect. Since the rebellion of a lady in this matter can cause great disruption in a family, the Prophet (sws) made it clear upon the guardians through both his words and the measures he took that they must not take any decision in this regard without her consent. If the lady wants, their decision can be revoked.
Ahadith do not provide independent rulings, rather they should be understood in the light of framework established by the Quran and the Sunnah and all ahadith on a particular topic should be studied before reaching any conclusion. This is the viewpoint of Ghamidi Sahab on Nikah. (For Further details, please see: Discussion 79037 AND Discussion 69727)
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For viewpoint of Hanafi Fiqh, please refer to the following Article:
Women Nikah without Wali - Hanafi School