Does he need to be there? Is it a financial issue? He sounds very immature however this happens sometimes with men and since you are not together he may feel that he doesn't need to do anything. It is sad really however if you are not with him and its not financial I would tell him to leave or you will have to accept the way it is and not depend on him for anything. That is the only other way.
I was a single mother for 7 yrs and had a similar issue but we were not living together and I had no help. It was hard but here I am with my daughter turning 11 tomorrow.
Sorry you're going through this. Your situation is not an easy one to be in.
I can tell you as a recent first-time dad myself, I really didn't know what to do most of the time on my own. I was in awe watching my wife take care of our daughter. This natural mothering instinct just happened in her. It doesn't happen like that for guys. We have to be taught how to do this. I think that's what makes your living situation so difficult. You're really not in a relationship with this guy where you can comfortably teach him the "ins and outs" of caring for your baby.
I agree with ticked. If you aren't together and he is driving you crazy and not adding to the picture in terms of your caring for the baby, I'd ask him or MAKE him leave.
If he is not able or willing to take proper care of her, he is not safe to leave her with him.
I would think about what other support you have in your life and consider that it is best to have him out of your home and rely on other people that will actually be of help to you.
Best of luck to you. Some men are simply sperm donors and never live up to the role of true father which is sad and their loss.
Sounds like it better off if he not even there