My boyfriend will always be in love with his ex even though he lies about it. What do I do?

My boyfriend and I have been together for a year. He and his ex broke up 3 yrs. ago. From the beginning of our relationship until now I was under the impression that he hated her. He claimed the whole time we were together that she was his reason for not trusting women, being hesitant about falling in love, etc. because she "cheated on him, used him for money, and in the end robbed him blind". well i found out that he is the one that sent her a friend req. on facebook a few mths after we got together, (which he lied about), then i found a couple wks ago that he posted on her wall calling her my "pet" name such as (bub) sorta like pookie, anyways, it also said "long time no see..." i wondered how i could of missed this, well he deleted it from his activity stream so i wouldnt find it. then i noticed a couple days ago that when he puts something sweet on my wall, (which is rarely ever) and its usually vague, but WHEN he does, he deletes it to from his activity stream. so if its general wall comment to me, doesnt delete it. if its sweet, says hun or love ya or something, he deletes it. like hes afraid somebody else will see it. as though hes ashamed, and he is hiding the fact that he put something a normal man would put on his girlfriends wall. AND THEN, i found them sending emails back and forth. hers wernt very personal, just general. his were more pathetic, like "i was just talking about you today,...why havnt' you responded back yet? ..." THEN when i confronted him about this, he lied, but since i had already figured he would lie, i had printed out my proof, so he said "ok, i swear i dont have feelings for her, i love you, i want to marry you, you are the girl for me, i wont talk to her anymore" literally 2 days later, i found a msg. from her, replying to him. he deleted the msg. he sent her so i couldnt find it, but i found her reply before he did, hence busting him. of course he lied about this w/ the most convoluted excuse ive ever heard. it was "my friend has my facebook login info saved on his computer, he must of got on my profile and been sending her the msgs." this didnt register w/ me, so then i finally found out, yea that was a lie, even though he still wont admit it. and then i found out from one of his friends that he gets "giddy" when his ex's name comes up, and this friend said he loves her, always has, and always will. SOOO what do I do? I've confronted him, he swears i'm the one for him, he loves me, he wants to marry me, yet why don't i feel like he is truly w/ me, 100%? I feel like i gotta constantly worry he is going to cheat on me, (even though as far as i know he hasnt done) or leave me if this ex wants him back at some point.I contacted her, she said they dont like each other in that way, etc. yet she doesnt really know what hes been doing, acting like, saying. so i know he is in love w/ her still (or so i think), but she claims she doesnt want him. im sick of being lied to, i dont know what to believe. I'm supposably his world, he lives w/ me, yet, he lies about everything. where hes going, who he talked to, and our intimate life has diminished majorly in the past few mths. to where its about once a wk and i have to be the initiator, the one that always wants him, but he says, "sex isn't important to me, i just dont care if i have it or not. but i still like sex, i just dont need it" (keep in mind, we are in our mid 20s.) what the hell is going on in my relationship? and did i mention he claims he HATES cheaters, he would never cheat, etc. yet hes the one lying, talking to his ex, still in love w/ her, and not giving me the affection and intimacy he used to.