Yeah, I doubt Solas is immortal. Er. We need a new name for immortal. He's immortal, but he can be killed. Its possible that if he was killed, part of him might be able to escape in the same way that Mythal was- but Mythal is still a shadow of what she was. I doubt she could ever truly be considered her own entity again. Similarly, whatever Fen'Harel really is would likely be lost.
For most of the game, he doesn't seem to have any additional powers beyond what a 'mortal' mage would have. Otherwise I'm sure he would have abandoned ship in Redcliffe, and not get tortured for a year. Unless he's going for some sort of oscar as far as charades go.
I finally remembered another word I was looking for in regards to the immortality talk!
Solas, and presumably the elven pantheon, are immortal but not invulnerable. They're the type of immortal where you'll live forever unless acted upon by outside forces... like a sword to the gut, for example. Or a red lyrium infection.
And then there's invulnerable immortals, which I don't think there's a true example of in DA. Cory's close, but invulnerable technically means unable to be hurt, period. You can definitely hurt him - even kill him - but he just transfers his consciousness to a new body (until you disrupt that ability, and then he can be killed permanently).
Maybe a good descriptor for Cory's type of immortality would be indestructible instead? Incapable of being destroyed... except for a loophole, of course.