There are other threads here on "moving in" together that might be useful. Try doing a search under that title to see what you find.
This situation seems like an incredibly bad idea... red flags all over with this one. I think she should be out on her own with either people in a living situation that she is not dating or on her own. She seems to be a user to me. Talk about not standing up for yourself.
I would be concerned about this situation in terms of your partner. I think if this were me I would be very firm of the changes to my involvement in his life. It sounds like he is not about to take her in however, but I would be concerned also.
As to getting to know her? She seems to be not interested, so I would just let it alone. She knows you are available to talk, that should be enough. It sound suspicious to me however.
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