Is he still in love with his ex or even cheating on me with her?

Ive just found this page and I have a question that I need to find an answer to. I have been seeing this man for about five months. I do like him very much indeed and we have a great time together but the point is that our relationship is rather complicated. For what he told me, he was in a relationship with a woman for 5 years. After 3 years she got pregnant with his baby. He told me that their relationship was a disaster and it was merely about sex, no love or anything like that. But since she got pregnant, he stayed with her and tried to make it work even though all his friends and family kept persuading him to leave her because according to them, she was no good. I don’t know her but he described her as a selfish woman who doesn’t care about anyone else but herself. They broke up after those 5 years when he got home one day and there was already another man with her. He said they broke up in August last year. So when I started up with him in April this year, I thought he could be over her after those 9 months. The thing that always bothered me was that he wasn’t able to talk about her nicely, which leads me to the thought that he still isn’t over her. Also he said that from August when they separated, they only talk about their kid and that there is nothing going on between the two of them. Anytime I asked him if he was sure he was over her, he snapped at me that he hated her and she made him sick. That was weird enough. I found some texts that they exchanged in February this year when he apparently wanted to get back with her, said he still loved her, there was rather sexual content, he asked her if she was okay with the sex she has with her new bf, she replied she wasn’t and he offered to book a hotel room for the weekend and leave. First she agreed but then texted him she didn’t wanna cheat on her new guy so early, told him to find a new gf and it all finished with her saying – once you have a new girl, and you feel like cheating on her, let me know. We can start seeing each other again. But now I can’t do it.
What do you think I should do? I know the texts date back to when I didn’t even know him but it breaks my heart that he may not be over her. And also that he lied to me. He kept those texts for half a year while there was not a single text from me. I know it is not easy for a man to admit he was or still is heartbroken but I have no idea what to think about this. PLEASE, POST ME SOME ADVICES, ANY… I will be grateful for anything. Thank you.