So, is this a bit like the in Latin, with "nonne", implying that the interrogator thinks the answer to be the affirmative, and "num", implying that the interrogator thinks the answer to be the negative.
Well, not quite. "Nonne"- and "num"-questions imply a special answer, forming "rhetoric questions". The German "doch" isn't in the question, itself *is* the answer or just a statement (because it musn't follow a question, it also comes after (negative) statements, to show, that the second person thinks different about what was said). In most cases the "doch" is unexspected by the first person, so it's quite a not forseen more or less surprising statement.
This is FANTASTIC by the way. I think this is exactly the kind of Non-English example that he wants to see.
So I want to introduce another idea, which is common in some languages (German, Spanish, Japanese), but not in English. I'm speaking about the two meanings of the English "but" (well, at least from a German/Spanisch/...-standpoint there are two meanings).
The first one is to make a strong contrast and can be found after positive and negative sentences, like
(1) My father went into the hills, but my mother went to the valley.
(2) He isn't my special one, but he is a friend.
In German this "but" would be "aber", in Spanisch "pero", in Japanese (e. g.) "-ga, ...".
The other "but" is to make also contrasts, but more in the way of "instead" (that means, it contrasts the maybe supposed thing with the true thing, correcting it). Therefore this "but" can only be used after negative sentences, like
(3) "Hamlet" wasn't written by Dickens [as you seem to think], *but* by Shakespeare.
(4) He isn't my special one [as you seem to suppose], *but* he is my brother.
In German
this "but" would be "sondern", in Spanisch "sino", in Japanese (e. g.) "-naku, ..."
English is the only language I know, where these two concepts are put together into one word ("but"), so if Na'vi would do it the same way, I couldn't avoid the feeling of having it an English touch.