My baby is 3 months old and likes to babble a lot - when I speak to her she seems to be having her a conversation with me. Are we actually talking? Does she understand anything I am saying?

I think your baby has discovered her voice and is experimenting with it! Though I don't think she can comprehend what you are saying at such a young age, she is likely able to recognize your voice. Just continue "chatting" and singing with her. She sounds like a joy to be be. Also, if she has not started laughing.. I've read that this is the period where you may hear her first laughter. Laughing is also one way that a baby learns about his/her own voice. Enjoy!! :)