Yoshikuni----I remembered you mentioning something similar back in The Athiest/Christian post. So am assuming here, that you've haven't become a Christian, in a public sense of the word.

Given her deeply religious background, she probably sets pretty high standards for herself in keeping with church teachings. Teachings differ from denomination to demonation but they pretty much agree on a Christian marrying another Christian. We're not talking about marriage here. It's just that maybe she might be trying to follow these teachings/rules, hence she sets boundaries like "Friends only". I'm hazarding a guess here that this is the reason why she is holding back. Also, the church can put immense pressure on their members. Christians can be amongst the most critical and judgemental of people.
So that's my answer to #2

As for #1, I don't think there's anything wrong with you. You must like her enough to defend her :-) However interest wanes if you don't get a positive response. You're you. Don't become a Christian just to win her over.