She says she loves me, but is she for real ?

Well it seems a little weird. If you say she is like kind of addicted to you. Also the fact that she "knows" the bible does not mean anything at all. She can know the bible but don't live by it at all. One month is NOTHING to know how a person really is... you just have to get to know her a little better. But for what you tell she might be serious about the marriage stuff. becasue she has child and she might be looking for a support for her...