Sounds like your new baby is really coming around and as far as biting goes - sometimes cats just love to give love-bites even though they may be a little intense sometimes. My daughter's Siamese cat acts the same way - he'll be purring and rubbing against her and then all of the sudden out of the blue he bites her and pretty hard too. I don't know what to do to discourage this - just be aware and try to keep from being bit. I find this is really common in single cat households - my cats display similar behaviour but they usually give each other love bites and leave me alone