Yes, they can.
Men and women are separated so they aren't distracted from their prayers.
the role of Muslim men is to earn money for their family women to look after the family
All obligations and requirements per Islam religion that should be maintianed and followed by Muslim women are the same as that to be followed by Muslim men. Accordingly, you can refer to the question below on the fundamentals of Islam where all of them apply for both Muslim men and women.
Specifically Muslim men (as opposed to Muslim women) pray in the front and center of a Mosque. Muslim women pray at the sides or the back of the mosque so that their image does not distract the men.
Muslim Women are not allowed to marry anyone not Muslim. Men can but women cant.
No difference.
It is best to let a Mulim make the first move. They are different sects within Islam, so in order to give no offense to any, just let any Muslim make the overtures in greeting, and just follow along.
Muslim men don't fear women. It is the opposite. Muslim men are commanded by Prophet Muhammad and in Quran to be kind to women and to be tolerant and helpful to them. prophet Muhammad is the first who said that Woman is sharing with man the two halves. Muslim men don't fear women but they may fear to fall in mistake if gazing at them or committing sin with them that they are not allowed to do with women without licit marriage.
the role of Muslim men is to earn money for their family women to look after the family
the role of Muslim men is to earn money for their family women to look after the family
Muslim men can marry jewish and christian women. Muslim women can only marry Muslim men. So if by "love" you mean marriage then Yes. if you mean boyfriend-girlfriend then no, and thats reguardless of religion.