In need of advice

Hello! I'm probably overthinking right now, but the questions just keep popping in my mind I'm just searching for some answers. So a few months ago I met a British guy online, a few years older than me. I finish university next year and he's working.
I've never dated/been close to a Brit before so this is all a bit strange to me, I'm not sure if it's him or it's just the cultural difference.
We haven't defined our relationship yet and honestly, I do not want to. We met online after all, and I want to spend more time to really make sure that it's plausible and that we're both serious about it. For now I'm keeping an open mind to things.
But I can tell we both have feelings for each other, or else he wouldn't spend so much time texting and talking to me (or at least that's what I think!).
Here are the things I find weird. He never compliments me. I mean, I don't need him to shower me with compliments because that would have been too fake, but I'm a girl after all and I want him to say one or two good thing about me here and there, you know? It just feels like he doesn't think I'm anything special. And okay, that isn't really a big problem because I can totally live with no compliments. The other thing is, I think he doesn't like to talk about the problems that we have. When we fight, he usually says "okay whatever, let's move on" or something like "Why do you like to turn everything into an argument? I'm tired of it". I just want us to talk things out and solve the problem, and not let our communication issues get into the way of our relationship. I don't know why it's that hard for him. When I confront/ask him questions when we're fighting, he often avoids them and never gives me a straight answer. It's getting a bit frustrated. Because I personally like to be in a relationship in which the communication is clear and open. Lastly, I don't know why but it seems that he never compromises. Sometimes it's just some little and petty things, but he insists in doing things his way, and never "yields". This isn't a very serious problem but it still kind of bugs me, I would like to know if it's a British thing or?

I know I seem kind of naive to take an online relationship that serious. But I feel like we have a connection and doesn't want it to go to waste just because of cultural/personality difference. Thank you so much!