I actually was thinking of the same codex entries that you drew on re: dwarves when I suggested that Solas and Mythal seem to have done something to them. The presence of statues of Mythal and Fen'Harel in the deep roads is pretty suspect - you really don't go to friend's home, knock down their gods and put up your own, as the elven journalist suggests. As for the other codex, in that old song that the journalist wrote, it seems that Mythal might have somehow given dwarves dreams, but since none of the ones we've met have dreams now, I'm not sure that what she did was a good thing... The Well of Sorrows easter egg seems to say that "Mythal speaks the calling," which just sounds like all sorts of possible bad, to me. I *hope* the elves didn't start the Blight but some of the codices and lore from DAI seem to suggest it's a possibility.
Regarding the Neromenians and what exactly they learned from the Old Gods, here's a digested timeline from WoT vol. 1:
-3100 Ancient: Records claim humanity arrives in Thedas around this date. This is disputed by scholars, who ask where humanity came from and why they left. (pg 11)
-2800 Ancient: The Old Gods are said to begin whispering to humanity from the Black City Golden City (according to the errata in WoT Vol. 2). They teach the Dreamers of the Neromenian tribes magic. Power shifts, and these Dreamers become both priests and kings among their people. (pg 12)
-1595 Ancient: Thalsian, also known as the First Priest of Dumat, is the first known person to wield blood magic. He claims to learn the art after personally communicating with Dumat, an Old God. (pg 14)
Learning magic and learning blood magic seem to have been two separate events in human history.
Yes, DA lore does say that only people with a connection to the Fade can practice magic, but it doesn't specify that they require a conscious connection to the Fade - only an ability to draw upon its power. It is also pretty clear that humans, elves, and Qunari all have an unconscious connection to the Fade, because they go there to dream. Solas tells the Inquisitor in one of the "I'd like to know more about you" conversations that *anyone* who can dream can become friends with spirits in the Fade, but few ever try. However, the fact that he says this suggests that anyone is capable of lucid dreaming; and to me, lucid dreaming seems only a step away from having a conscious connection to the Fade. But of course this also would mean humans and Qunari could have a conscious connection to the Fade since they can dream. Which means that I shouldn't assume that only elves ever had that ability, as you point out. However, if you are correct that humans and Qunari are altered elves (something I have also considered) then it really does become a moot point. I'll have to keep speculating and poring through the lore until DA4, it seems. Hopefully that'll make the years until its announcement and release pass quickly. ^-^
(As an aside, since the Neromenian Dreamers learned magic from Old Gods (powerful spirits?) in the Fade, and Solas tells us that anyone can make friends with spirits while dreaming, it seems possible that anyone who can dream could learn magic if they sought out the right kind of spirits while dreaming and asked the right questions...? Solas does say that the Veil is a lot more complicated than people think, and I guess he'd know. There's a codex too that suggests that the act of passing through the Veil is more about changing one's perceptions than a physical transition - see http://dragonage.wik...entry:_The_Veil)
Anyway! The whole Fade/magic connection is one of the really grey areas in the DA Lore, I find. And, people with no connection to the Fade can learn how magic works (Dagna) - they just can't actually practice magic themselves. DA Lore does state that magic courses through all living beings in Thedas, and that it may even be what gives all beings life. There may be some bombshells to be dropped from that down the road, hard to say.
I'm not sure that your point about the Avvar is relevant because the Neromenians were supposedly the first humans in Thedas, and there is no mention of any of the Alamarri tribes (from whom the Avvar descend) until -2415 Ancient, 685 years after the first humans arrived, 385 years after the Neromenians learned magic, and 820 years before the first recorded use of blood magic. However, I fully acknowledge that all the lore in the WoT books is from an in-world perspective and may therefore not be how things "really" are in Thedas.