Eesh, what a mess. Talk to a lawyer, and maybe even a counselor just to understand what YOU want. Is this guy on the baby's birth certificate? If not, it might not be a bad idea to keep it that way.
It's possible that you could have the guy sign a document surrendering his parental rights if that is what you want. If so, talk to your lawyer about this. It would possibly be good to have the child's grandmother in his life, if you trust that she is not as messed-up as your ex, but it doesn't sound good at all to try to have the dad in the baby's life, because he is simply (for whatever reasons, and the reasons don't matter) not trustworthy. His girlfriend and her attitude complicates things, but frankly he does not sound like a bushel of peaches even if she were not in the picture, and you don't want to be jerked around by his games playing and his failure to keep appointments and all.
If you do want the child to have some contact on the parental side, check out the guy's mother. You might even have a cup of coffee or lunch with her at a local cafe before she is scheduled to come with her son to see the baby, maybe you can get a sense of what she is like independently of her son. If she seems like a nice grandmotherly type, that could be a resource for you and your son in years to come. It's kind of hard to believe she is, though, given the son she raised.
In your shoes, I'd do some serious analysis about whether you want this bad smell in your life at all, and act accordingly. At the least, ask him to stop texting as though you are his girlfriend, and let him know SPECIFICALLY that the only reason you've been in touch is the baby. It will relieve his girlfriend's worries (maybe) and it will keep you clearheaded on your posture when you see him. You wrote "I found out he was with his girlfriend and her son the whole day," that sounds like you have some jealousy going on and that is not good because you should be as unconnected to him as you say you are. It shouldn't have mattered if he was with his girlfriend or at the library, the irritation was that he didn't come over when he said he was going to, not why he didn't.
Anyway, have a talk with a lawyer to see what obligations you have; I can see you are concerned that you need to keep the guy in the loop, but I don't think that legally you are obliged to do that. I don't even think there would have been anything wrong with you not telling him the baby came, frankly, unless of course you intend to try to file for child support from him. His criminal history and instability give plenty of cause not to want to have to interact with him, though, even child-support money would hardly be worth the grief.
How did it go at the lawyer? I see you wrote in August that he had been to see the baby about three times, that sounds like you changed your mind on him not being involved. Did he drop the girlfriend, or change something else about his life? If nothing has changed with him, why did you have the visits?