Most Helpful Girl
Well I'm first going to point out that if he has told you he loves you but he is willing to cheat multiple times then sadly he might not mean it. When you love someone that's the only person you want to be with and can see yourself with 20 years later. Or at least to me that's what it is. And if he isn't willing to respect you by you asking him not to hang out with certain people then you should definitely talk to him about that since if he truly lived you he'd be OK with that. But lastly I can not tell you for sure whether he is cheating on you but there is a possibility that he is. And also if he was drunk and he texted a girl with perfect (for how he types) grammar then he most likely wasn't drunk. My ex was drunk many times and texted me and he could barely type and he didn't even have a touch screen that would make it easier to mess up on. So all in all there is always a possibility that he is cheating. Talk to him or even other people of he won't say anything and try to find out. Worst comes to worst then break up with him.
Hope this helped :)