should I give him a shot?

so recently i’ve been dating this guy. We’ve been talking for almost two months now and I lost my virginity to him. (He doesn’t know I lost it to him though) I really like him and I think he’s great. However, mid talking to him I discovered that he broke up with his ex of 2 years, 3 months before we started talking and that he still sorta is in contact with her. This really scared me of course and I tried to break it off in order to protect myself from falling for him more than I already did. Though he didn’t let me and reassured me that she is out of the picture but that she is his best friend and of course he would want to stay in contact with her. Which I totally understood, but supposedly he would try to reach out to her, and she wouldn’t reply because she is ghosting him part of the reason I guess why they broke up). Anyways I took his word for it and since have been continuing to talk to him. We talk all day everyday and hangout as much as we can. We’re not official but we’ve established that we’re solely only speaking to each other. I’ve brought up the fact that i’ve wanted to be exclusive with him a couple of times and he told me that that’s what he eventually wants but is just not ready for that yet since he did just get out of a relationship. Which I get so again I put my pride aside and told him i’d wait. However there’s a few suspicious things that he does that throw me off and make me wonder if I should wait it out like I committed to do or just run while I still can. One being that whenever we’re with each other he hides his phone from me. (Now it’s not like I want to be searching through his phone but when we’re cuddling with each other and he deliberately has to face the other way in order for me to not see his phone, it causes me to wonder, when I go on my phone easily right in front of his face). Two, from what i’m aware of he still tries to reach out to his ex and gets depressed and sad about her once in a while. Three sometimes he goes MIA on me a little (like he’s doing right now) and won’t do his regular phone calls at night or will reply hours later when texting with me (which isn’t normal of him). I know this may all sound crazy, since we did just start dating, but I can’t help but feel like this all when I express to him how I feel and he is constantly trying to reassure me that he likes me a lot and to continue to talk to him. It sort of feels like he’s just telling me what I want to hear and I could possibly be a rebound and someone to help him get through this rough patch of heartbreak from his ex. (Also what he reassures me he’s not doing)! I’ve never been in a real committed relationship and this is the farthest i’ve gotten with a guy so I don’t want my anxious mind and overthinking to get the best of me and fuck up a good thing. Once again he is great and we have a lot in common, I just don’t know what to do...