dating a boy in love with his ex

I’ve been with my boyfriend for nearly a year now, he’s a good guy and I love him very much. He dated his ex for almost 3 years, so of course she was a big part of his life. I understand that, and I totally understand him having memories with her and thinking about her sometimes. About 6 months into our relationship, I found out he had been EMAILING her things like “I miss you” and “I wish you would give us a chance” and things like that. My heart shattered at the thought of him loving her more, and I felt as though he was only with me because she didn’t want to be with him. I was angry, and bringing up the topic brought fights. He was obviously still in love with her, and she was heavily on his mind. I was so angry because I started to feel like a second choice, and almost like I was competing even though she wasn’t involved at all. She wasn’t answering his messages, which made me feel better but he had been doing this behind my back our entire relationship. He would even send her pictures of me sleeping and say things like “I have her right here but all I want is you”, or if we travelled somewhere together he would send her pictures and say he wished he was doing this with her. He would even go as far as tell her lies like I was pregnant or we were engaged in an effort to make her jealous and get her attention. When he found out she was dating someone else, he was furious. Watching this and finding out and reading everything he sent her broke my heart. I was angry and betrayed. He promised me he didn’t love her anymore, and that he just thought of her sometimes and was angry how things ended between them and wanted closure. I didn’t believe it but I let it slide because I am deeply in love with this man. He promised to no longer contact her. Fast forward months later, I spend a month at my moms. When I come back, I find out he had been emailing her while I was away. I was so angry, and yet again flooded with emotions. I didn’t want him to be with me if he was still in love with another woman. He was angry she reached out and told me, and after a headed argument about it, the first thing he did was reach out and tell her she shouldn’t have told me and that he was angry with her. She doesn’t get his emails anymore, but he doesn’t know that and I will not be the person to tell him. His first girlfriend and him are still friends, and at first it didn’t bother me because they have been broken up for many years and I am still friends with an ex of mine. And then I found out that SHE sent him ‘risky’ photos of herself, even though she knows he is dating me. Now I’m skeptical about their relationship and I get angry every time I see them talking, especially because he won’t let me see their messages because he wants his privacy. I understand his privacy is important and I respect it but the exception of her. I always let him see my messages with my ex, because I have nothing to hide. Anytime I get upset about either girl, he gets mad and an argument is started. He claims I’m psycho and shouldn’t react so harshly and that I don’t have the right to be upset, even though I have every right. I love him so much and I do everything I can to make him happy, but at the end of the day I truly feel like he’s just settling. He makes a point of telling me he wouldn’t want to be with anyone else, but I know he would go back to that one girl if she wanted him. And sitting with that hurts so much because I would chose him over everyone. I just wish he loved me as much as he loves her.