It's not confirmed what happened to Mythal/Flemeth. My best guess is that they fused together, or joined together. They seemed to be on good terms. I believe Solas wants the Elves to regain their former glory, and he wanted to free the Elven Gods to accomplish that. So he has the orb after waking, but he is too powerless to use it. He gives it to Cory, who uses it for his own ways, and Solas now has to find another way to free his buddies.