Mostly they are allowed to, yet, you need to know that in Islam there are many sects such as Sunni and Shii, whithin each you will find several doctrines and fatwas on such issues (i.e, in Sunni sect you may find Hanbali and Shafei). In main stream Sunni sect women are allowed to wear nail polish, only they have to remove it for Woudou: the ritual of washing certain parts of the body in preparation for prayers. In Shiite, most commonly It's allowed even during Woudou. Some very minor doctrines prohibit it totally.
when women have their periods, women wear whisper to stop the blood from staining their clothes.
No women do not wear cologne it's called perfume
Women's Wear Daily was created in 1910.
Pentecostal women normally do not wear a vail.
the women in Mumbai wear saris and Punjabi dresses
Sunni
Yes, both do. Men mostly wear dreadlocks, but women wear them, too.
All Muslim women are supposed to do so. It is not particular for Shiite. It is worth noting that the wearing of the niqab (which covers the front of the face) is actually more common among Sunni women than Shiite women, if only because of the laws and culture of Iran as compared to Sunni-majority Arabian countries.
women clothing
Sunni
almost 30 percent of women do not wear under-ware