Yes, Muslim men can marry non-Muslims - it's a way of bringing them into the fold. But a Muslim woman marrying a non-Muslim is not allowed.
Is she religious at all? Does she wear a head scarf? Is she observing Ramadan (which is going on right now)?
My young French friend is an observant Muslim, he doesn't smoke or eat OR drink anything - even water, from sunrise to sundown during the month of Ramadan. He's also abstaining from sex (although, technically, as a single Muslim guy I don't think he's supposed to be having sex outside of marriage anyway, but I could be wrong about that).
So, WII - if she's at all observant, OR if her male relatives are, then dating her could be fraught with peril.
