Question intonations vary among cultures. I'd use whatever mother-tongue intonation for questions which you use daily.
It's always interesting to me that cultures keep tone, not languages. It's an unproven theory of mine, but it sure seems to me that midwestern USA English consists of the English language with 19th century German tones. This tendency is one reason why I don't put much stock into trying to recreate the ancient tones of Greek, as the "Restored Attic" pronunciation scheme attempts. First, I think it is far fetched to think we can reconstruct the tones of a language from notations made to the text. Secondly, I imagine that most of the Greek speakers of the ancient world, were non-Greek and used whatever native tones they grew up with as an overlay to the Greek language.
While I'm relaxed about tone, I think that stress accent and consistent pronunciation of the letters and combinations of letters is very important. You can intone a word like "syllable" any way you want, and I'll understand immediately. But if you say "syrrable" or accent it on the 2nd sylll'able, I'll have to restate/translate what you said in order to comprehend it. But if you and I had different pronunciation schemes (regional accents, if you will) and if you consistently say "syrrable" soon enough my need to translate will fade.
That's why, after a short time, a person can listen to Restored Koine, Modern Greek, or Erasmian pronounciations and not have huge problems in comprehension. What does negatively affect comprehension, is inconsistency. For example, a common Erasmian tendency that does trip me up is inconsistently pronouncing omicron, sometimes like a short O, other times a schwa, and other times a short A. I think the fault here is not the pronunciation scheme itself, but that Erasmian is/was mostly used by instructors and learners who employed a system of learning that makes pronunciation mostly unnecessary. In other words, they were sloppy with their own system because it didn't matter.
And so, to come full circle, I think you're right, Cheiromancer, to think about things like this and consider how to pronounce things. Ancient Greek is, after all, a tongue.
I will babble until I talk. ετι λαλαγω...