I don't think there should be rules for that. You just do it when it feels right. As for seeing the real person, I do think that it helps but a lot of people see the real person before living together. It's a matter of opening to the other. Living with the person just helps seeing how the person is on a daily basis
Yes, you can move in together too soon. You should be dating for long enough to know that it's serious. I would recommend at least 4-6 months of dating before moving in together.
I don't think you can leave it too late, unless you wait until after you've married. You really don't see the true person until you live with them. what are you going to do if you move in after marriage and find you can't stand the person?