Ex boyfriend being too friendly?

My ex and I were in a serious relationship for a year. He is a very ambitious man and moved to another continent for work. I am 31 and didn't want to wait around for him to sort out his life, and long distance was hard, so we broke up. Within weeks of our break up, he had a new gf. His new relationship moved super fast. They met each other's parents within 2 months, and they were writing I love you on their Facebook walls and she tags pictures of them together regularly. 4 months into their relationship, we met up when he was in town and he cheated on her with me. I felt guilty about the situation and we agreed it would never happen again. He has not been in town since then.

He has been with his gf for a year now. We have stayed in touch as friends and do video chat about once a month. Our conversations were pretty neutral before but lately he has been complimenting me and joked about us getting married. He also emailed me on New Year's day to say he wants to chat. I thought maybe he had broken up with his gf, but I checked his Facebook profile and they are definitely still together and she is still posting on his wall about how amazing he is.

Question:
1) Do you think his behaviour is inappropriate
2) Does it sound like he wants to get back together, or is he trying to play me?
3) My ex comes across as a really nice, innocent guy. His friends, family, and girlfriend all think he is a really good person, but I think his behaviour says otherwise. It annoys me that people don't see him for who he is. What should I do? I still have feelings for him, but I'm not sure what he wants, and I don't know if I could be with him given his character flaws. If he cheated on his gf with me, he could have cheated on me too.

He cheated on his GF with you. So IF you did get back together don't you think he'd just cheat on you with someone else. And to be honest, he sounds like a real class one d.ickhead so why are you even bothered?

1) Definitely, yes.
2) I think he's a jerk and is trying to get in your pants again, and/or he's too immature to deal with serious commitment so he sees you as an escape route.
3) He isn't really nice and innocent, is he? You know better. You should cut contact with him altogether, as you should have done a long time ago. He's nothing but trouble.

C'mon...

You don't really need us to tell you that his behavior is inappropriate.
You were a convenient piece of ass when he was in town, and he wants to keep you hoping, so that you will be again when he's in town next.

And as boisdevie said - even if he got back together with you, he'd just cheat on you sometime, when a convenient piece of ass presented itself.

I don’t see why you’re hesitant. I’m sorry to say but if his girlfriend doesn’t know you were with him when he came into town, how can you be certain he wasn’t cheating on you before you two separated. I mean he did find a girlfriend awfully quickly. I think you should ask him if she is aware that you two video chat. How does he react? Does he answer this question by turning it around and asking why do you want to know? It doesn’t sound good. You shouldn’t expect to get back together with him. If anything, I think he’s trying to soften the mood with you so that the next time he is back in town you have a brief flirtation period to build on and thus make a connection easier. The more I type the more I’m convinced: this guy is a jerk.