The black city was already black when Corypheus entered

According to Corypheus, yes. However, it is also possible that the black city went black the instant the magisters entered. Mother Giselle also says that Corypheus might have deluded himself into thinking the City was black all along because he could not face the fact that he angered the real God. However, there is a codex entry where a dwarf talks about going deep in the deep roads, encountering the Architect from DA:A who helped him, and another dwarf talking about seeing 3 "tall darkspawn, dressed like kings" (basically other ancient magisters) arguing about a "city gone black", then 1 darkspawn running away while the other 2 fought and eventually one of them ate the other. Unless they were all delusional, the city was either black all along or became black instantly at their touch.

Solas and Flemeth are ancient elven Gods

Flemeth was once an ordinary woman who welcomed the "essence" of Mythal. According to Flemeth, however, they are as separate as you are from your own heart. So, for all practical purposes, Flemeth is Mythal. Solas is Fen'Harel, but it's unknown whether or not Solas was once an ordinary Elf who welcomed the "essence" of Fen'Harel, or he is Fen'Harel himself.

If you don't know, in elven lore, th anciente Elven empire fell from the side of Tevinter, and the Elves called to their gods for salvation but received no answer. The reason for this is that Fen'Harel tricked both the Elven Gods (Mythal being one of them( to lock themselves out in the "Beyond" (Which is as far as we know the Elven name for THe Fade) and tricked the Forgotten Ones (gods who exemplified negative traits such as Death and Malice) to lock themselves away in the "Abyss". The Elven empire then crumbled, and turned to what we have today. The Dalish, who have tales of tales of tales of tales, and the city elves, living in poverty.

However, in the game it's revealed that the ancient Elven empire wasn't as sunshine and roses as it's depicted in various modern accounts. It had a slavery system (and the slaves were marked by the vallaslin face markings which the Dalish wear proudly in misconception), and according to the book The Masked Empire, it didn't have a culture that was much different than present-day Orlais. The reason for the fall of the empire, however, was not Tevinter, but the elves destroyed themselves from within by infighting, Tevinter apparently just finished the job.

It's also revealed that Mythal was murdered by someone (not Solas), and not sealed away (by Solas), as previously thought. Seeing as she is in good standing with the Dread Wolf (Fen'Harel) in the epilogue, there is even more to this story. Since there is a codex entry that speculates that Fen'Harel wasn't strictly a god of trickery, but a god of rebellion (based on the interpretation to a word relating to him the Dalish elves use), there is speculation that Solas was a part of some kind of rebellion, then later actually sealed the gods away for unknown reasons (which seem to be regular Elves - but an order of magnitude more powerful than any ordinary elf).

Anyway, some banter with Cole indicates that the Eluvians might have something to do with Solas' imprisonment of the gods. It's nothing concrete, but a good lead.

The eluvian goes to other worlds

All eluvians go to a single place: the Crossroads. Some eluvians from the crossroads may lead to other realms like it, but if you ever enter an Eluvian from the outside world, you will enter the Crossroads.

Also; fyi: The epilogue takes place at the Crossroads as shown by this video. This will be important later. And you need to know that Solas actually absorbed Flemeth, not the other way around. He actually speaks through Cole if you talk to him after the main story, but you can't discount Flemeth as there is reason to believe she is not 100% dead yet, and she also said to Morrigan that "a soul cannot be forced upon the unwilling", hinting she may have given herself to Solas willingly.

Corypheus also wanted to use the Crossroads (the place where all the Eluvians lead) because he needed another way to enter the Fade physically, as he messed up his first one. The Crossroads is a realm very close to the fade, and is said by Morrigan that if someone was able to take down the "ancient barriers" they could have another way of physically entering the Fade. This will be relevant later on.

So what we have now-

• Solas was in some kind of turmoil that affected the ancient Elven empire
• Eventually, he seemed to actually seal the Elven Gods away in the Fade, for unknown reasons, but the story told about him by the Dalish is innacurate
• Solas then presumably goes into uthenera (Elven cryo-sleep)
• Thousands of years later, he awakens
• Now, speculatively, he wants to return the Elven Gods he sealed from the Fade
• The orb Corypheus used was given to him by Solas because he was not "strong enough after his slumber" to activate it, so he gave it to Corypheus
• The orb gives you the ANCHOR, what the Inquisitor has. It gives you the ability to freely enter the Fade any time you want, and gives you the ability to walk there physically without any injury
• Solas, presumably, wanted Corypheus to activate this orb, then possibly kill him (or he was expecting him to die from the orb itself- not the explosion) and take the ANCHOR for himself (just as Corypheus tried to take from the Inquisitor but could not because seemingly after some time the anchor ties itself to whoever is wielding it)
• The orb, however, was dormant for some time, and all of that power it cultivated for so long resulted in an explosion that triggered the Breach
• Solas was seemingly not expecting this, as his only intention was to trick Corypheus into activating the orb and then somehow acquiring the anchor for himself
• Solas is also surprised by how Corypheus survived, because he was not aware of his power to jump bodies
• Solas, seeing what he has done, rushes to the scene of the crime to try to help and that's why he's present at the epilogue
• The story unravels
• The story ends, the orb breaks
• Solas, now lacking any way of entering the Fade physically (due to the orb being destroyed at the end of the game), is now at the Crossroads with Flemeth, presumably because this is how he is now looking to enter the Fade
• Solas absorbs Flemeth, Flemeth presumably giving herself to Solas willingly

There are a couple of important unanswered questions:

• Solas must have known who Corypheus was; how, and why did he seek out Corypheus exactly? Could he not have gone to Flemeth? Corypheus doesn't recognize Solas if you take him to the final fight btw, he speaks to him, but berates him. Since Solas gave the orb willingly to Corypheus, he didn't steal it, how did their interaction go?
• Why exactly did Solas want the Anchor?
• If Solas did imprison the Elven Gods such a long time ago, presuming he suddenly wants to free them now, why? What is his endgame?
• Why did Solas absorb Flemeth, and why did she give herself to him willingly?

Red Lyrium, which was found inside of a Dwarvern Tiag, has the blight?

Yeah, and it's revealed that red lyrium is alive to some degree. Only living things can be affected by the blight. Don't overthink this, though. You get the blight by simply being near darkspawn or anything that has the blight- you don't have to interact with them. As that particular dwarven thaig has golems, it's a safe assumption that it was open at at least one point during the First Blight, meaning the lyrium inside of it could have been tainted by darkspawn.

Since red lyrium is ordinary lyrium + the blight, it also functions in the same way. It spreads by proximity, and that's why there's so much of it in game.