Domestic violence..long but please read. Advice?

So I've been in a relationship for 4 years it's been very rocky. He's cheated on me before( emotionally, sending sexual messages and photos, video chatting). He claims that he has stopped doing all that, but i don't have a lot of trust in him obviously for good reason. We have a child together so that's the main reason I've tried to make things work. Well tonight I just calmly asked him if I could see his phone. He immediately got very defensive saying why, and laying it on the floor beside the couch. I told him I was leaving and not to contact me again if it doesn't pertain to our child if he wasn't willing to let me see his phone. He still resisted but I ended up getting it. I looked through his messages there was nothing..so I went to his call logs and it showed his recently deleted messages which included some texts he claims were from a coworker. They were talking about what kind of coffee one got, and he was asking if she was dressed warm cause he didn't want her to be cold. Also there was a text that was one asking the other about a porn binge. And he sent a photo of my child to her today. When I asked him about that he got very angry and threw something that hit my child in the face and had her bleeding on her eye brow. I heard him throw something, and then herd my child start crying, I didn't see it hit her and don't know what it was. He was trying to say he didn't do it, but obviously she didn't start bleeding for no reason. I then had him acknowledge that his actions are the reason she was hurt. He then said that he was gonna kill himself tonight, I told him to do whatcha gotta do. That I wasn't going to beg him not to. I'm so disgusting and don't know what to do. I told him I am no longer his girlfriend so do what you want. I don't receive child support and really need the money. I'm currently living with my parents, I moved out of our apartment together in Feb. after he punched a hole in the wall again talking about his infidelity. He claims he'll get custody because I don't currently have a job cause I care for my child 24/7, he sees her for a few hrs once or twice a week. I have photos of the hole in the wall, and my child's bloody eyebrow. Is this enough to prove he isn't a fit parent? He gets mad because I don't let her stay the night with him, I do not trust him. I lived with him for 1.5 years after our childs birth, and he was never up at night to help me. When she was a new born and started crying I recall him putting the pillow over his head and saying "oh my god" aggravatedly. Should I file for child support? He's barley keeping his bills paid as it is and makes like 50,000 a year.

All this is coming from a man who claims to love me? That's some BS, not love.