Yes, Felassan was definitely Solas' agent and Solas killed him as confirmed by Cole's words "The slow arrow breaks in the sad wolf's jaws", for the crime of seeing Briala and the others as People. This is why I'm pretty sure he took back the control of the eluvians without needing to cross her path, probably after absorbing Mythal. Morrigan was able to control her eluvians independently of Briala, as could Mythal. Even the Qunari were able to control their bit separately. So it would seem that the information given to Briala was a lie, not surprising since it came from Imshael, and all she did was activate the network and have control over her localised bit. Solas needed to intervene because given the likely link between the Crossroads, the eluvians and the fate of the Evanuris, he couldn't have numerous factions blundering around in the network. The amusing part is that if you recruit Michel, you can get him to spend time with Solas telling him what he remembers about the network and the events in Masked Empire. Nothing like aiding the old wolf is there? I always thought it odd that I wasn't allowed to chat with Solas while he was in Skyhold about this but of course not everyone might choose that option. I also thought it odd that after Morrigan shows you her eluvian you don't have the option to chat about it with Solas because that would seem the natural thing to do, given his interest in all things elven and ancient. Mind you, I think he still did go and inspect it on the sly.
What I do wonder is if he invited Briala to join him, she would agree. After all, unless he admitted as much, she wouldn't know that he had killed Felassan and the latter had set her up to co-operate with him, telling all those stories to inspire her to rebel against her station in life and then her using "Fen'Harel Enansal" (The Dread Wolf's Blessing) as her password. Certainly if she was put in charge of Orlais with a puppet Gaspard, then she would have little to lose in vacating the throne and much to gain after Trespasser, since with the Inquisition diminished or disbanded there was no longer the threat of the Inquisitor intervening should the nobles/Gaspard attempt a coup against her. With all the elves running off to join Solas, she would also not have the threat of her underground army to hold over the nobles either, particularly if she could not longer move them around with ease.
Still, in some people's playthroughs she would be executed and thus dead anyway, so I really don't think she is going to feature much in future plots, particularly since we are moving northwards and without the eluvians she has no way of moving around Thedas quickly.