1) Is cyvasse inspired by any particular games?
A bit of chess, a bit of blitzkrieg, a bit of stratego. Mix well and add imagination.
2) In your "mind's ear", do accents from different parts of Westeros map to accents from real life, or are details like the Dornish drawl primarily a matter of background color?
Yes, Westeros has regional accents. I played with the idea of trying to depict them with phonetic misspellings (and indeed I do a little of that, with some less educated characters), but that way lies madness. I try to suggest the accents with syntax and taglines instead.
3) There are historical mysteries -- not just recent matter which might have a bearing on the current plot, but older things that are a part of the background -- which have interested a lot of readers. Do you know the answers to all these purposeful mysteries, or do you only decide such details when you actually have to do so?
Depends on the mystery, I suppose. I know the "answers" to many.
4) There seem to be hints in FEAST that Dornish commoners have a greater sense of nationalism (for lack of a better term) than we see in other areas. There are plenty of smallfolk yelling for war following Oberyn's death, for example, which I don't think we've ever seen before since the smallfolk tend to prefer peace and plenty. Timeon tells Brienne to send him to Dorne as she's killing him, as well. Is this intended, or am I reading too much into these examples?
Dorne was a nation apart from the other six kingdoms until a hundred years ago, so, yes, they have a stronger sense of nationality.