How long should it take for me to trust my husband again?

My husband and I have been married for only 9 months and earlier on in our marriage he made some foolish mistakes which in turn made me feel like I cannot trust him. He lied to me about going to see a female who claimed she got pregnant by him (the jury is still out on whether or not it's his) when he went down there. And in the early months of our marriage, he continued conversations with a certain female online who lived in the same city as we do (who consequently he met on the plane ride back from his weekend with the other girl who says she was pregnant). They talked about seeing each other and he went so far as to refer to me as his girlfriend and was saying that he didn't think things would work out between us. I looked at then times the emails were sent and it was while I was asleep in our bed pregnant with our child; at 4 something in the morning, he thought of this chick to email her. After that was handled, there was another situation when we were in the bedroom and his cell phone rang. He looked at it for a while and said he didn't know who it was I asked him if it was a blocked number and he said yes. Later that night I looked in his call log and saw that the call was actually from some female that was saved in his phone book. He claimed they were friends, but because he lied to me and couldn't answer the phone and talk to her with me sitting there, I figured there was more to it. I later found out that they dated in the past. I told him that I didn't want him talking to her anymore which he didn't respect my wishes at first. He continued talking to her and she continued to say inappropriate things about how she misses him so much and she wonders what her life would be like if they had never split up. I saw these messages and told him to end it now, which he did (but the hard headed girl still tries to contact him). And recently, he reconnected with another girl who was only a cut buddy ( call). I saw no reason fo him to be talking to her now that he's married and why try to be friends NOW? I tried to go in his email and see just what it was that they had to talk about but he had already deleted them and for some reason he couldn't recover them (he was able to recover my email from moths ago but mysteriously he couldn't recover his). My trust for him is at rock bottom when it comes to him and females. I check his phone and emails regularly which he gets mad at me for but given what has happened I feel is justified because I know he's not going to just come out and tell me if he's talking to anyone else. And in all but one of those cases the females found out he was married when I told them. He hasn't done anything physically with them, but I feel that what he has done was just as bad. So, I would just like to know how long will it take for me to trust him again. And this is just another question to put out there for married men and women: are you okay with your spouse contacting their ex while you are married? I say while you're married as in they didn't talk to them as friends before you got married but they talk to them now that you're married. Please help, I love my husband dearly and I want our marriage to work. Despite what this may make him look like he is a good man. These things happened early in our marriage and he has admitted to his wrongdoing and moved past it.