I didn't say he meant you make you cry, as you didn't mean to upset him.
But you both got upset by things the other said thinking they were funny, while taking the piss out of each other.
It's a good thing he apologised for hurting you.
And while he shouldn't have told you to fuck off, have you meanwhile apologised for upsetting him in the first place?
A proper talk is in order, I think. While you should make it clear that you won't put up with such answers from him, you both should address how to make sure the piss taking out of each other doesn't end up ruining the relationship.
It may be funny the first time, but it will grate at some point, as you are discovering.
I don't think it's a matter of whether you are ready or not for a proper relationship.
It's not your problem that you cried. If you were upset, that's fine. He responded appropriately and should take more care in future not to upset you in that way.
You should be more careful about taking the piss out of him too.
That's something for you to work out as a partnership.
As for the fuck off reply, I'd make sure to let him know that it was inappropriate and that I expected respect, and for him to let me know he was hurt, rather than name calling. I'd let it go for now, but would be vigilant and wouldn't put up with more.