WoT has a section about the Fade and different races. Qunari claim they don't dream, whether or not this is true or simply because it's forbidden by the Qun is up in the air. Apparently Qunari are rarely found in the Fade, and that's used to support the idea. Although it's funny that the Qun could simply outlaw dreaming and expect it to be enforced. That dreaming is forbidden at all is odd. If it's another remnant of an old order, it makes a little more sense.
I think the Old Gods/Archdemons are probably shapeshifted elven gods rather than possessed dragons, but I agree the properties of dragons and their blood are likely why they were bred into the Qunari, whether they were originally elves or otherwise. Whether the Kossith and/or Qunari were bred for the exact same purposes given by the Qun is another thing...
Speaking of purpose, which is kinda big with Qunari, the Dalish concept of Sulevin, "purpose" still nags at me at how familiar it sounds. The Cradle of Sulevin was also where I noticed for the first time how similar the Qunari crosshatch symbol resembles the elven crosshatch design.
Sten, along with Morrigan, recognized that the Fade section in Origins was a dream, unlike Senior Enchanter Wynne or the dwarf Oghren. Maybe this is because the Qunari lack some sort of proper connection to the Fade, and he could see the actual green clouds and floating rubble, and was, "Oh, I read about this in Beresaad prep school. It's one of those 'dreams'."
Or it's because he's a smart cookie that's dreamed as much as you or me, and enters lucid dreaming when he recognizes his dead comrades. But, in defiance of Qunari teachings, he clings to it, because 'it's a good dream'.
The Saarebas are held in chains and have their tongues clipped and are executed if not within sight of their Arvaraad because the Qunari are so paranoid about demons speaking to them from the Fade and influencing them. How could they fear demonic possession if they don't have a connection to the Fade?
(HOW DID THAT DEMON POSSESS THAT ANCIENT DWARF PRINCE BACK IN THE CALLING? INQUIRING MINDS WANT TO KNOW!)
Which brings up another interesting thing. The Qunari are obviously terrified of magic. I can't help but think of it like the alcoholic couple's children drinking only water, or me using real butter. I'm willing to bet that the kossith are some kind of magocracy, or have a demon problem. Koslun and successors went far, far the other way to ensure they didn't repeat their parents' mistakes.
Which had to be great when they landed in Thedas and discovered a less powerful magocracy that they could stomp on. 