Those questions, as far as I know, are never really answered in the game.
Solas tells you right after the fall of Haven that the orb is from the ancient elves, and he's probably telling the truth about that. Flemythal says that Solas is responsible for Corypheus' getting his claws on the orb, but we don't know the mechanism by which this happened (did Solas walk up and hand it to him? Did he put it conveniently in Corypheus' path? Did he broker some kind of bargain which Corypheus later broke?)
We know it's an object of great power, enough to rip open holes in the Fade when combined with whatever else Corypheus was doing to Justinia. But we don't know it's exact nature, nor what Solas was intending to do with it once he got it back from Corypheus.
My personal thought is that Flemeth's body was dying, and Solas was going to use the orb to somehow save her life. But he couldn't succeed at that. Instead, he has taken Flemythal into himself - he's now the host to 2 (possibly 3) god-spirits, and his next move is to find ways to house them. I think he is grieving because he knows that being host to Flemythal will change who Flemythal is - like if getting a kidney transplant made you more like the donor and less like yourself. He knows his friend will never really be 'his friend' again, but he's still going to try and save what parts of her he can.
If you go back and really pay attention to what happens in All New, Faded for Her, I think what Solas says about spirits (if you save his friend instead of killing her) is directly applicable to Flemythal's fate post-game. He says that particularly powerful spirits, and spirits which have had a great effect on the world around them, often come back; albeit in an altered form. And both Flemeth and Mythal are known to quite a few people in Thedas. I really believe we're supposed to take what he says in that quest line and apply it to Flemythal. Especially because a more accurate translation of 'Asha'bellanar' (what the Dalish call Flemeth) is not 'Woman of Many Years' but rather 'Woman of Eternity.'