My Orthodox Jewish grandmother married a Reform Jewish man.
Yes, but NOT Orthodox Jewish women.
Orthodox Jewish women cover their hair in public once they're married. One way to do this is to wear hats.
Of course they can
Only the Orthodox Jewish women wear headscarves. Some Orthodox Jewish women prefer to wear wigs rather than headscarves. Some non-Orthodox women will wear a kerchief over their hair when attending a synagogue service. The reason for a woman covering her hair is modesty. The hair is seen as a thing of beauty (Talmud, Berakhot 24a), not to be exposed to passers-by.
It is not permitted by Jewish law; and in Orthodox Jewish weddings the seating is separate for men and women.
No. That would be some Orthodox Jewish women. Not Muslim women.
Only in women's groups
Only Orthodox Jewish women do that.
It's an Orthodox Jewish place, and Orthodox Jews practice gender segregation.
Yael Israel-Cohen has written: 'Between feminism and Orthodox Judaism' -- subject(s): Jewish women, Orthodox Judaism, Religious life, Judaism, Feminism
Orthodox Judaism doesn't allow "staring" at women. Orthodox Jews practice gender segregation to prevent "indecent" behavior.