Is this normal British behaviour?

I (26F) met a guy in Singapore (27M) last November due to his work trip and I was just doing solo traveling. I currently live in Sydney while he’s in London. I’d say that we had a good connection, he looks like a very awkward guy but alcohol helped. I didn’t expect that he’ll keep in touch after we part ways, he went back to UK while i went back to Aus. it wasn’t much, like just short messages on random days. he’s normally the one taking a long time to message back but i didn’t really care because i know how busy he can get (he works in finance) and we all need our own space and avoid interaction with media when we unplug.

2 weeks ago, we were messaging each other and it looks like he found the time to message back immediately as he replies within a minute. his messages looks like he is drunk, denying it at first but it mainly consists of him telling me he misses me and he’d like to visit Australia next year. i don’t know if i should believe him at the time because like i said, he’s drunk.

Last Thursday, he suddenly called me around 8am Syd time (assuming it’s 9pm in UK). He’s telling me he’s at a Christmas party and asking me what the time right now is in Sydney, then he suddenly just asked me ‘Do you miss me?’ i fear he’s drunk, again. to summarize everything, i told him i miss him as well and he told me he’s frustrated why i only message him once a week, he called me a liar when i said i miss him too. I was so confused like what does he even want? but i was chill about it, i told him to not overthink it, i really do miss him and i want him to visit Australia. I also was busy with work because i did some night shifts lately as I’m a nurse. He went on to tell me the things we did when we first met and kept saying things like we’re gonna hop on some bars, that i should take him to some beaches around here, we ended the call on a good note. I messaged him after that call asking him if he’s alright, he said yes and apologized for what he did because he just missed me. i explained why i only message once a week because i do respect his life, i don’t want to come off as clingy and he suggested for me to just text him (don’t know if he meant to reach out to him more?) then he just suddenly cracked a joke after that, which i’m not used to. but i’m pretty much aware of the British behaviour when it comes to banters. So like what he suggested, i continued to message him more, he reciprocates back, calling me ‘babe’ sometimes. I do like the guy but i’m keeping myself grounded because we’re literally on the other side of the world.

I don’t know what to feel. I am confused tbh. I haven’t dated a British guy before but i heard that they are quite reserved when it comes to these. I don’t even know what kind of relationship we have lol, it’s an odd one. and i fear that we’re not yet on the level of talking about what outcome do we want out of this.