As for the swearing and shouting rather than being able to have an adult discussion, it’s always been that way, right from the early days, honestly the word CUnextTuesday washes over me like as if someone is asking if I would like an extra helping of desert. It’s not an attractive part of him but it’s something I’ve always known about and I could have chosen to end the relationship years ago if it was going to be a deal breaker. There are days when I choose to let things go rather than having him shouting and swearing but there are other times when I feel strongly enough about something that I will go for it too!! But that takes a lot of effort and some things really aren’t worth it...
Honestly, this is not right at all.
I know, I grew up like this, and to me it was normal to hear certain things, but now I know that it's abusive. His behaviour towards you, to call you a cunt so easily and readily and scream when you mention anything IS abusive.
I'm really sorry, but it just is, there's no other way around it. He uses his anger to control you, to weaken you so you don't mention anything you don't like or upsets you as you don't want that reaction, so he can do what he wants.
And this waking you up, that's also part of it. Controlling when you get up, making you more sleep deprived, and then texting as you weren't as happy and as chatty as he wanted at 5am. It's all part of his controlling behaviour towards you.
You've asked him already, he ignores it and continues to wake you up and chat about banal things and then say you weren't quite what he wanted at that time too.
Honestly, he's an abusive man. Do you want your little girl to hear him calling you a cunt? You say it's normal to you, do you want that to be normal for her, and then the partner she ends up with will also treat her like a piece of shit? It's no way for him to treat you, and you must know this deep down.