Why has my ex boyfriend started reaching out to me when he has a girlfriend?

Me and my ex haven't spoken for 4 months, since he cut me out when he got a new girlfriend... Then around 3 weeks ago, he messaged me (via his mums facebook - he's deleted his) saying he was sorry and hopes I don't hate him. He then asked for my number, which I gave to be civil. Plus I kind of want to talk about what happened between us at some point, because I think it will help me move forward. He text me straight away but just quoting a movie we always used to watch together and nothing else.
Then, a week after that, he text me again saying that he wishes I never hated him. He wished me all the best and said I was a good girl. I said to him I didn't hate him, I just hate when he has done. Then about 4 days after that, he came into my workplace (a small cafe) where only 4 of us work. So he knew I would be there/speak to him. I was friendly to him, but he seemed really uncomfortable. He didn't say a lot, all he said was that he thinks one of our mutual friends fancies me because he gave me a discount on my car and that he thinks he looks like a frog? So random. Other than that, he really didn't say anything. He was just kind of pacing up and down and wouldn't look at me. Then when he did look
at me, he gave like a sad smile?
Im just a bit confused as to why he has been doing this? What is his reason behind reaching out to me after 4 months of no contact. He is still with the girl that he went with right after we broke up. Surely it's abit inappropriate to be messaging/ visiting your very recent ex when you are dating someone else. When he was in my work, his phone rang and it was a guy and my ex lied about where he was to the guy on the phone. Maybe im wrong, but to me that kind of shows that he knows he shouldn't necessarily be in there?
Why has my ex boyfriend started reaching out to me when he has a girlfriend?
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