I don't even know where to start typing.
Please take everything I am saying seriously and not as just being critical.
1) Don't move in together. There are many, many reasons for this and not just spiritual. Couples who co-habitate are more likely to divorce later on than couple who do not. Don't just take my word for it. Go read some of the research literature out there on living together before marriage. You will find enormously more negative than positive things. I don't have the time right now, or I would provide you with tons of sources. I honestly believe that living together before marriage is like setting yourself up for failure. There must be some place else your girlfriend can go live if her mom is kicking her out. And that is a whole different issue there..... why is her mom kicking her out? Normally parents don't just say "you are grown and have a job, so get out." Usually it is because their adult/ semi-adult children are not able to abide by the rules of the house. You don't have to tell me the reasons she is being kicked out-- just think about it yourself and contemplate if this is a woman that you think you should be with.
2) You mention that your gf became a Christian and now is turning away from a lack of positive Christian mentoring. I believe that this is a big problem everywhere. BUT.... do you really want to find yourself married to a non-believer one day? Is it possible that she never truly committed herself to God in the first place? You mention that she has no remorse for her sins. I realize that coming to Christ does not mean that people change overnight, but to have no remorse is still bothersome. When you come to Christ you are supposed to repent of your sins. Has she ever recognized her sin nature and repented? (By the way, ALL my questions are rhetorical. They are things for you to contemplate and answer honestly within yourself.)
3) There are a lot of things that you mention about your gf that are bothersome to me. Normally, I wouldn't care, but from your other posts you seem to be a decent guy who has his head on straight. I just hate to see you make the same mistakes in relationships that I have. There are things you write about your gf that sound similar to the guys that I have wound up with. Quick to anger. No remorse. Liberal. "Christian." Jealous. Etc. (Although sometimes jealousy is justifiable and an individual should listen to their significant others opinion on staying away from certain others.) Notice I put Christian in quotes. I did so because it seems like these people are making a commitment to Christ and in reality there is no commitment nor desire for one. Anyone can say a prayer and profess to be a Christian, but it doesn't necessarily make them so.
4) You are questioning about if you should break up with her. You admit that you are finding other females attractive (especially a certain female). You say that you are finding that you and your gf are drifting apart. I would say that maybe it is time for you to end it. You are not married to her (otherwise I'd suggest counseling). Moving in would be a bad idea, and you are uncomfortable with the idea anyhow. I would break things off now before it is too late and things have gone too far. Can you imagine what it would be like trying to end things with her while sharing a living space? She might very well walk out and take all your property with her. Or put your clothes in the bathtub and pour bleach on them. (This stuff happens, and you said she has anger issues.)
Anyhow, I'll stop babbling now. If you want, I can delete my post and tell you to just pray.
But, you know that you should be praying anyhow. Have you ever thought that God has been whispering to you about this girl all along and you were just too infatuated to hear him? Sometimes God whispers, but we are so focused on what we want rather than what God wants that we ignore him.