Did Ancient Greek have a rising intonation for questions?

Answer 1

Ancient greek was actually a tonal system, so the short answer to your question is technically yes.

The long answer is that ancient greek interrogatives (who, what, where, etc) often were marked as tonally higher using an acute accent (example: τί meaning what?) but that's only part of the story. A vowel could also be marked with a grave (τὶ) which meant you should speak in a lower tone, or a circumflex (τῖ) which was an up and then down tone. Greek also had both smooth and rough breathing marks if the vowel started the word to denote whether the vowel had an "h" sound in front or not.

So if you look at the first two lines of the Iliad:

μῆνιν ἄειδε θεὰ Πηληϊάδεω Ἀχιλῆος

οὐλομένην, ἣ μυρίʼ Ἀχαιοῖς ἄλγεʼ ἔθηκε,

You can see that for θεὰ in line one, the α would be pronounce as lower tonally as compared to μθρί in line two, where the ι would be pronounced tonally higher.

However, while this is probably how Ancient Greek people would have pronounced it, in most western, non tonal speaking countries, Ancient Greek is often not spoken tonally. So the long answer is technically yes, but not really as it is currently spoken!