Are women allowed to lead men in prayers? Are these historical examples true? A woman led the funeral prayers for Imam Shafi'i (a respected Muslim scholar). In another stance the Holy Prophet (sws) would visit an elderly woman. The male servant of that woman would use to call the adhaan (call for prayer) while the woman herself would lead the prayer (http://shams.za.org/womenclaim.htm )
Also should women be allowed to pray alongside men in the mosques as they do in hajj? Or should they be segregated?
There is no clear guidance on the issue in the Islamic Shari`ah. Therefore the matter has been subject to difference of opinion among the Muslim scholars some of whom consider even a woman leading men in prayer. We believe that a woman can lead other women in congregational prayer. From the scholars of the past Imam Shafi`i and others are the exponents of this viewpoint. You already know the report where the Prophet (Sws) is told to have appointed a woman to lead the prayer in her family. Also please go through the discussions: Why Can't Women Lead Prayers?
The historical facts you have referred to have reached us in the form of individual reports which of course are not absolutely reliable. However, we see that most of the historical records are transferred through the very means. Therefore, we often consider such reports if they are not negated by more reliable sources facts and are not against sense and reason and do not violate the basic religious teachings.
Since Islam does not allow free interaction of men and women for it can lead to consequences detrimental for the purification of the believers. In Muslim societies one would observe that a separate part of the prayer place is reserved for them. However, it is not the basic condition for the acceptance of the prayer of either of the men or women. In extraordinary situations as in Hajj women stand alongside men and this practice can be adopted in other than hajj as well.