Isn't this the "NO Spoilers" general discussion thread? Isn't your first post a spoiler right off the bat?
As to that...
"Solas claims the Old Gods are not related to the elves. But he implied killing them would make things worse, even as they sleep underground."
So? They don't have to be related to elves for him to guess that it might have bad consequences.
From what I know so far (I haven't played Descent yet), the "song" they hear from the taint compel the darkspawn to seek out and awaken an Old God, which in turn feels compelled to create a Blight to wipe out all life. (And I'm guessing they can "sense" the Old Gods underground, since they're otherwise mindless monsters, yet they seem to have a general idea of where to find the Old Gods.)
As long as the darkspawn search for the Old Gods beneath the Deep Roads, they spend most of their time and energy away from the surface and don't focus the bulk of their attention on harrowing living beings. If the Old Gods all die, the darkspawn might "sense" it or figure it out eventually, then harrow the dwarves and the surface en masse. While there might not be anymore Blights, that might not matter when the bulk of the darkspawn horde (which cover every inch of the Deep Roads under every inch Thedas) come up to harass the surface for the end of time, since they've got nothing else to do.
"Dumat and the other Old Gods taught magisters, like Corypheus, how to break into the Golden City."
So the Chantry and the magisters claim, but we don't know for sure. The magisters could have figured it out on their own (through magical experiments and whatnot) and just believed their gods inspired or indirectly directed them (the way most Andrastian characters in DAI believe the Maker "indirectly directed" the events that led to you being declared the Herald of Andraste), and the Chantry could just be blaming the Old Gods for the magisters' folly.
Besides, how does the Chantry "know" what the Old Gods did and didn't teach the magisters? Is the Maker somehow connected to the Old Gods in a way the Chantry doesn't realize? Why aren't you accusing the Maker or Chantry of being in cahoots with the Old Gods?
"If they're responsible for releasing the Blight then why is killing them a bad idea?"
Again, searching for the Old Gods is what keeps them underground. If there are no more Old Gods to find, what's to stop them from focusing all their attention on harrying life on the surface? The surface will soon become as desolate and tainted as the Deep Roads. (Or, worse, whatever "intelligence" directed them to search for the Old Gods could give them a new directive that'll threaten all life.)
"If the Fade is so wonderful how could the Blight have come from there?"
Solas never claims the Fade is perfect. He prefers it to the physical world (after seeing many of the horrors that mortals come up with and the ways the living have corrupted otherwise benevolent Fade spirits and presences, I can't fully blame him), but he's also aware of its faults, risks and dangers. In fact, when he talks about the Fade, if the Inquisitor gets a little too excited and praises it too much, he'll be quick to remind you that the Fade has its dangers just like the physical world.
"The Blight is some toxic by-product at the center of the Fade. It's all the bad mojo that accumulates from the dreaming activity."
Or it could be a by-product of all the negative emotions and/or expectations of mortals. As Solas shows the Herald in-game, the Fade is a reflection of reality and the emotions and perceptions mortals experience in the physical world. Benevolent spirits are born from benevolent emotions, and we've seen in both DA2 and DAI that benevolent spirits are twisted/corrupted into demons thanks to the negative emotions and expectations from mortals. The Chantry itself teaches that the Golden City was corrupted by the magisters' own "sin." While they believed it was a direct punishment from the Maker, it and/or they could have become corrupted from the moment they set foot in it, just like how Justice became corrupted into Vengeance the moment he set foot inside Anders' mind.
I mean, the ancient elves came in and out of the Fade for millennia and never tracked anything bad home. Then elven society fell and humans enslaved the elves, and somewhere over the centuries the Veil between the Fade and physical world strengthened. It's possible that this caused understanding between the physical and spiritual world to decrease, which caused mortals to fear and distrust spirits more (well, that and try to use and manipulate spirits more; all that demon-summoning and enslaving couldn't have been good for the Fade's spirit population any more than the elves'), which likely caused the Fade to become a more threatening place. Then some very wicked and corrupt humans tried to set foot inside the Fade (an area they were warned not to go into) and then they tracked something bad home.
To me, that's just proof of humans stepping in something they shouldn't have stepped into, not those gosh-darn dirty elves masterminding everything.