Relationship troubles

My boyfriend and I fight most days. We've been together for a year now. Mostly the fighting is about him not trusting me and accusing me of cheating or going behind his back, which I never do.. But it's been like that since the start of the relationship, I'd walk into the room and he'd be really angry at me not telling me why and when I finally got it out of him, it was because he'd gone through my phone, emails, laptop, everything.. And found something he didn't like (me talking to a boy for example). 

Now days he doesn't even like me going to work because he thinks I'm cheating with my boss. -.- I've put passwords on everything because it upsets me that he goes through my Instagram, texts, photos, snapchat, everything.. As soon as he gets a chance. (He'll read this if I'm not super careful).

I have terrible self confidence issues because one time he said I needed to lose weight, so I did and spiralled into an eating disorder, down to 39kgs at my worst. I've since regained all that weight.. And my boyfriend doesn't say anything like that at all anymore, but since I'm the same weight I was when he did say that, I feel uncomfortable and worry what he thinks (he says he doesn't care but it's just how i think). 

Which brings me to my next problem, we've moved in together this year. We've hardly had sex. A great perk of being with him was that I was so sexually attracted to him, our sex life was great! Now.. I can't remember the last time we were intimate like that.. It makes me feel unwanted and undesirable. It's been months. I've asked about it once and he just says that's how relationships go, it's not all about sex anymore. But surely after a year it's not normal to completely stop having sex? He also said he's too old. (He's 25...)

Lastly, I overheard a phone conversation with his mum. I wasn't snooping, I was in the car right next to him so I couldn't help hearing.  She was expressing her sadness that another girl now has a boyfriend, saying things like "did you see she has a boyfriend? Such a shame, I almost cried!" When I asked what that was about, he told me that she always tries to get him with this other girl... I was heartbroken. 

Sorry for the life story. I don't have anyone else to talk to really, I don't even know what I'm asking.. Just for advice I guess. Thank you so much for your time.