''Why Muslim women not allowed in Masjids''.........?
At the time of Muhammad (pbuh), the women prayed at the rear of the building while the men were at the front; however, they would have been within earshot of the imam (religious leader), and any men entering the mosque would have had to pass them. A saying attributed to Muhammad is: "Do not forbid the mosques of Allah to the women of Allah". Also, on the Hajj, the mandatory pilgrimage to Mecca, men and women pray side by side. In most modern mosques, however, women and men are segregated into separate sections, where they perform ablutions (wuzu) and prayers (salat). Any women's groups or classes will normally be held here too. Usually there are separate doors for men and women, with the children entering with their mothers before being led to madrassa (religious school).
Second point is why not with men:
Muslims customs does not allow to pray with mens, it is knows as PURDAH.
The veil must be followed. Why veil, the reason: Other peoples, that (husband and brothers left.) should not see the women, because the eyes makes every thing wrong thinking and to avoid any sexual feelings on the mind. Therefore, veil,purdah system. Black-Burkha why wear: Black colour is not transparent so thus wearing black will be considered.