Solas is doing this because Mythal is now loose in the world (the blue female figure from the Well of Sorrows), and she wants her revenge. Solas wants to stop her, but for that he needs the anchor. This also plays into a worldstate where the Inquisitor drank from the Well. Solas can't have Mythal using the Inquisitor against him. Removing the anchor removes the Inquisitor's power.
Solas has also orchestrated a plot to end the Inquisition, since this also removes the Inquisitor from the world's chess board. He has recruited elven servants (who have seen his "god" power and now believe in the elven pantheon) in Orlais and Ferelden to pass on information to their respective nobles about the Inquisition that will cause concern among said nobles.
The Qunari we fight are a new faction. The Qunari in Par Vollen consider them Tal-Vashoth, but they consider themselves true Qunari because they have learned the truth about the Kossith and their own origins, which the Qunari in Par Vollen refuse to admit, as it would damage the "Body". This means The Iron Bull can be sent to stop them as Hissrad, or he can join the Inquisitor naturally as a Tal-Vashoth. This way, both paths from Demands of the Qun are represented. Also, the alliance with the Qunari is left intact if the Inquisition agrees to help. There may be an option to expose the Qunari's secret at the end of the game. Who told the Qunari this secret? Solas, naturally. He hates the Qun.
The anchor was created by Corypheus, so I don't think anything is affecting the anchor directly. But it was spreading and killing the Herald initially. It was Solas who created wards and saved the Herald's life. The anchor being destabilized could be a natural occurrence, but I can only guess that Solas is willingly allowing the anchor to spread so that the Inquisitor will be more inclined to pass it on to him. So while he may not be affecting the anchor per se, he may have done something to the wards he placed way back at the beginning in Haven's holding cell while the Herald was still unconscious.
The elven ruins are side quests to try and figure out what is happening with the anchor and the magic that the Qunari Serrabas are using. The elven spirits we see are spirit guardians similar to those seen in Witch Hunt when we go to Cadash thaig (Cad'Halash, according to Eleni Zinovia).
It is also possible that the nobles we see in the trailer are all Orlesian. I didn't see any Fereldens, though it's possible that the voice artists we heard who voices Teagan was indeed voicing Teagan. But in either case, these nobles may fear that the Inquisition is provoking the Qunari, and will bring all of southern Thedas into a world war. Again, this would be orchestrated by Solas, and it would be easy to do.
This does seem like Solas' style; tricking people into doing what he wants, and screwing both sides over in the end.
Only part I'm not sure on is how Morrigan plays into it. If she drank from the Well, Mythal might use her to stop Solas. She might even be the dragon we see in the trailer. I don't think Solas and Mythal are working together, otherwise Solas would not have been so defensive over the suggestion that he drink from the Well. Had they been working together, he could have simply trusted Mythal to release the compulsion afterward. Then again, he didn't seem to know that Mythal endured until entering the Well chamber. But if they are working together now, then there is nothing to stop her from forcing the Inquisitor to give the anchor to Solas. So I doubt they are working together. However, if Morrigan did not drink from the Well, SHE might be working with Solas to oppose Mythal. She might blame Mythal for everything Flemeth did to her.
Another option is that Solas took control of Mythal, and now controls whoever drank from the Well. But this would kind of ruin the ending for those who drank from the Well. Solas would just be able to compel the Inquisitor to give up the anchor or otherwise support his plans.
But what a twist that would be, Solas takes over the compelled Inquisitor and rules through him/her, thus making the Inquisitor an enemy/hostage in the next game.
But this is all assuming that BioWare will stick to the established facts and not change things around with rewrites.