Should a Muslim woman marry a Non-Muslim man?

I am interested in converting to Islam. Last night I was telling my boyfriend about this and he asked me what is the Muslim perspective on marriage (we are thinking of marriage). I was like…you know, I dont know~! So I looked it up online and I read that Muslim women cannot under any circumstances marry a Non-Muslim man. It is because the man is the head of the household and the family would be under his leadership. A Muslim woman cannot have a household with a man with whom she does not share the same faith and values with. Im not gonna lie, I was a little sad to read this as my boyfriend is not a Muslim. And he tells me that just because he doesnt want to hear anything about the Christian church right now doesnt mean he is going to go running to Islam or anything else. (we both met in church and fell away a bit too). I was like okay okay, but I was thinking…”Allah works in mysterious ways!” Anyways these are my questions: 1) Can a Muslim woman marry a Non-Muslim man? 2) If I choose to follow through with converting to Islam, should I wait until he becomes more open to it? 3) Should I convert and just continue to date him and set the best Muslim example I can in hopes of him becoming interested?