1.It does matter Old god is gone when it transforms into Archdemon so you don't kill Old god at best you can argue you have killed Urthemiel but he ain't old god anymore.Ice and water aren't the same thing in first place that is why ice is ice not water and vice versa.
2.Pretty much false in first place flemeth couldn't locate them until Dai ,OGB was solely in morrigan hands (unless warden went through the mirror) she did good job with OGB , that she let herself bind to mythal is another matter what doesn't matter here as again she did good job with OGB and in fact either you or her had to do it in order to defeat corypheus.
1)You have to use the word "gone" with more precautions,the word is not a synonym of dead.
When the Old god become an AD ,the pure form of the old god is gone like you claim, but gone doesn't mean that he is dead, he is transformed, not killed,there is still something of Urthemiel inside that body.
If you play the Dlc darkspawn chronicles,you will notice that Mr. Archdemon is capable to speak,even if he is heavily tainted he still retain part of his intelligence,part of his consciousness,but he is mad because of the taint.
But the point is that after the sacrifice Urthemiel cannot return anymore,you remove every possibility for his salvation,alias you killed him.
btb this will be the last time for me to revisit this point
2)Pretty much is true

You're just defending Morrigan here without proving solid construct (i wish something more solid from you ,you used the timeline).
The point is,it doesn't matter when Flemeth come,if the DR is performed (basically if the Warden trusted Morrigan) then it's Morrigan responsibility to protect the OGB and not allow to anyone to steal his power
If Kieran lose the old god soul it is because of her mother's fault
(nope The Inquisitor have no fault in this put the inq aside from the equation he/she doesn't even know about the old god at that point and it is not even he/she responsibility)
the warden delegated to Morrigan the old god soul,not to Flemeth,but Morrigan failed in her duty and now Kieran's destiny it is in Flemeth hands,due to Morrigan mistakes.