To what extent has the notion of “nations” evolved in Planetos. ASearchofIceandFire has the word used 9 times, mostly about the Dothraki-nation and the nations they conquer, as well as the different nationalities represented in harbour cities. (Sorry if the Q is to vague or wide in scope. Thank You!)

This is actually a great question. And the answer is that nations very much refers to peoples rather than states, and it seems to be there somewhat. For example, the Free Cities other than Braavos do seem to care about being descended from Valyria, although not to the extent that recreating the Valyrian Empire is something that’s popular outside of Volantis. 

Westeros seems to have a sense of Westerosi culture – although they’re usually called Andals by Essos, which is interesting – founded on a single language (which makes no sense, but w/ever) and the respect for the old gods and the new. Even before you have the monarchy, you still have pan-Westerosi customs (guest right, trial by combat, kinslaying taboos), pan-Westerosi institutions like the Night’s Watch, etc.