Just to add my two cents to both Solas' agenda and his relationship with Lavellan;
(Spoiler) I think Solas had some part in why the supposed elven gods are gone hence his guilt but that it was more complicated since Abelas claims the Dread Wolf had nothing to do with Mythal's murder. Since slavery was confirmed to be a thing and he is suggested to be the god of rebellion, he might have either aided or outright fought with a rebellion against the other gods. Maybe he did do something that finally sealed them away. I also think he was a very different person than he is now as he seems to say, in banter, that a mistake he made was made by someone younger who thought he had all the answers.
(Spoiler) As far as I can figure, he is trying to undo his mistake by finding some way or another to bring back the ancient elves or maybe just the elven gods. He does not consider the "modern" elves be they city elves or dalish to be what he considers the People which makes sense. This especially explains his dislike of the Dalish who claim to be "true elves" but despite their arrogance, really know nothing and is essentially a reminder that the elven people have been reduced to tribals where they before had cities. They are also close-minded, a trait he has no love of.
(Spoiler) In short, it makes sense that he sees no real connection between himself and them based on features alone. It'd be like having two people from two very different countries with very different cultures and one telling the other that they have kinship because of a shared skin color.
(Spoiler) From some of his banter with Varric, it also seems like he cannot stand being the last of his "world" and that if he dies, then that's the end.
(Spoiler) His relationship with Lavellan is about him seeing that there is something more to the "modern" elves even if the Inquisitor rejects the idea of attributing their decisions to their Dalish heritage. Even if they are an exception to what he generally believes, they still have traits and a spirit that suggest potential (Need to find a better way to phrase it). Maybe they even give him hope that there's more exceptions to be found and that's exactly why he has to break it off and leave.
(Spoiler) In his post-break up banter with Cole, the latter mentions that "you are real and that means they could be" which I took to mean that the other elves could have the same potential as Lavellan and that he fears staying would make it too hard to do what he needed to, it'd make it too easy to just bury his mistake and built a pretend life on top of it.
I don't know if it is just me but there seems to be a foreboding tone that implies something might happen to current elves if the old ones were to return.
(I'll clean this post up, I promise. Add a few banter quotes)