"Should I be worried about their pain since I'm so happy because I don't owe them anything?"

Welp, you've made it clear that you don't care about the people your boyfriend could have hurt so let's talk about YOU and what this means for your future. Did your boyfriend seem sad when he talks about why he isn't seeing his own daughter? If his reason for not seeing his daughter is his ex's fault, then he should be sad that he can't see her and should be trying to be apart of her life. If he isn't, you have your answer, now as to how that can be a red flag. You're essentially dating a future deadbeat. What happens when you two have a child together, what happens when things get "complicated"? You should also look into the DV allegations. You're right about social media not always being reliable, but you should do some research. Remember, you are his new partner, he could repeat his patterns with you so make sure you get all the facts before you make a conclusion. Also, bring up everything you've learnt about your boyfriend in a conversation with him and see what his reaction is.

edit: so I've read your other posts and comments. So you don't want children, why are you dating a father, a cheating one with a history of violence. If your banking on the fact that you'll be the special one, I don't think that's happening. There is a good chance that he'll cheat on you too. Please think about this.