Well it does raise a good point. If Solas was watching the world from the fade, how does he not know Cory is immortal, or that Mythal was still alive? Surely he is not omnipresent and all knowing. But he specifically knew about the Battle of Ostagar...but not Flemeth's intervention in that battle. And he gave his orb to Cory at some point, so he must have been watching him as well, but didn't know that the Wardens were keeping him in a magical prision, and that Hawke had freed him and failed to kill him.
Did he think Cory's immortality was weak/ineffective and was no match for his orb?
There's a question how much he can see through Fade when it comes to Blighted creatures... not sure about the Wardens (as Solas describes us a perspective of what I assume to be our DAO protag and Alistair), but we do know that Cole is unable to peek into Cory's head and get a good picture. Apparently he's "too loud".
.. Which, you know, I think they kinda had to introduce as a device to prevent from Inky just asking Cole to describe him exactly what Corypheus is planning or something 
Still, I don't think they'd do it without a reason. Therefore the Blight might have a distorting effect on the Fade, perhaps?
There's also another possibility - a lot of Wardens AND Tevenes - use blood magic, and we do know from Solas that it makes it more difficult to cross to the Fade through dreams, or attracts demons rather than spirits. Maybe it's also has an effect on memory stored in the Fade?
Was Mythal hiding herself from him? Did he think she was just Flemeth, a powerful witch, or that there was nothing left of Mythal inside her?
We do know he's aware of Flemeth enough to travel to her hut, but we don't know how much he's aware she's also (at least partially) Mythal. But perhaps he was attracted there because he felt something familiar? Maybe this is also why he went to Ostagar - because there was a connection between the hut and the battlefield he could not quite pin?
Still, it's entirely possible that he knew there was something about Flemeth, but he never expected that the wisp that escaped... wherever she escaped from, might be simply too small to be significant. Flemythal on the other hand seems to do a lot to keep her status hidden though, so it's possible she was masking herself.
I mean... realistically, we can't assume that there aren't other beings from ancient past who she may want to hide from or lull into false sense of security perhaps. Like the mysterious ancient-elf-looking-red-vallaslined elves that attack people at the edges of Tirashan? Or what about Geldauran and his ilk? Or Forbidden Ones? And when we ask in the Fade if she knows what Inky is fighting with, she says that she knows more of it than we could imagine.
... In fact why are her - and Morigan's eyes - are described in game-files as blight eyes? :/
Did he think Cory's immortality was weak/ineffective and was no match for his orb?
Possible? Perhaps he expected that raw power of the Fade has adverse effects on the Blight itself? I mean, we do see during final fight that even after a long time under Corypheus' control the magic of the Orb stayed uncorrupted, turning pure green the moment Inquisitor ripped it from Cory's grasp. Then we see Inky open the rift which easily rips and destroys Corypheus' body.