Well Im personally a bit dissapointed... I wished there were more background story about the inquisitor. Sure at the moment im a carta dwarf but whould be more interesting with a better background story as to why a carta dwarf were there in the first place... the "Spy" deal dont work too well. Id rather see a background story involving trying to make deals with the templars and mages at the meeting. (as an example). Since i dont really feel that much for my dwarf inquisitors backstory.
Even if i might agree som plot holes are left open around how the events at the temple of sacred ashes acctually occurred their quite easy to fill with logical conclusions.
1. My answer to why the divine acctually could end up in that situation, might be becouse of the grey wardens being present. Concidering the mage and templar rebellion, aswell as the problematic situation involving the seekers. The grey wardens might have either acted as her personal guard or demanded an audience with her prior to the meeting. Its highly possible concidering Grey Wardens high regard in Orlais, to get a personal audience without guards. Leliana does also mention her suspicion of wardens very early in the storyline, long before the acctuall memories return to the inquisitor.
Corypheus most likely already were present at the temple of sacred ashes, prior to the acctuall meeting. Concidering Corypheus control of the corrupt wardens it whould be quite easy for the wardens to get divine Justinia into an appropiate position. Chain her with blood magic and significantly hamper her strenght to resist, which obviously also makes it harder to cry out for help.
As for the inquisitor;
Dalish Elves and Carta Dwarf - Spying around and ends up there by coincidence.
Humans - Highly devout family and might per chance be the first one to open the door after Corypheus started speaking (Hes way to loud). Aswell as Trevelyans have close ties to the templar order so he/she might acctually feel something amiss concidering the blood ritual used to bind the divine.
Mages - Probably sensed the ritual or the disturbance in the fade.
Qunari - Was hired as extra protection by the chantry, so might be that the inquisitor as the leader took personal responsibility as to check on her.
As far as we know the meeting itself might not have started yet or had already been held. But most likely this happened before any meeting started.
2. As the magic binding the Divine most likely were blood magic, Justinia should have a natural resistance too its influence. Chantry sisters do not go trought the same rites as the seekers. But concidering the divines duties and strong devotion they should still achive a high grade of resistance towards magic influences. Concidering the friendly spirit in the fade, i whouldnt be suprised if Divine Justinia acctually had encountered a spirit of faith. It also explains why the spirit retained her memories and assumed her shape. It whould also explain why Corypheus needed her as a sacrifice to activate the anchor. Concidering the enormous amount of power the spirit contains.
If we look at the Divines situation. Being bound by strong blood magic and being alone, she most likely were conserving her strenght to get answers out of corypheus. Then as she saw oppertunity used her last strenght to push the anchor out of corypheus hand.
3. To be entierly honest i think both the Anchor and the orb of destruction, can become fused with the user. But as Corypheus is a darkspawn, the taint might prevent him from physically merging with either orb. To activate the Anchor corypheus most likely needed a spirits power, but since corypheus is what he is... its probably very likely that his mere presence whould corrupt stronger spirits into demons as their easially corrupted by mortal influence. Divine Justinia whould in that case be a perfect vessel to extract spiritual power from and thus activate the anchor. Why the anchor kept being active might be becouse of the inquisitions frequent use of it in attempts to seal the rifts. The best explaination whould be the inquisitors first attempt to seal the breach stabilized its power and full control were finally achived.
The anchor were then further enhanced after corypheus tried to remove it using the orb of destruction. That attempt most likely resulted in that the anchor absorbed power from the orb of destuction, thus making Corypheus orb unstable. Which explains why the orb broke in the end. Solas interest in the orbs, might be becouse the former elven pantheon might had used "his orb" which probably were the anchor (unclear if Solas / Fen' Harel / Dread Wolf, refers to the anchor or the orb of destruction in the epiloge). But i assume the orb Corypheus possess is a relic from a forgotten one (Dumat). Solas also whitout any explaination shows the inquisitor how to use the mark, which further enhances the theory of Fen' Harel being the former owner of the anchor.
4. Well concidering the tempels layout from DA:O. Having guards outside of the door might had caused suspicion, or the inquisitor could had forced his way trought the guards if any. Especially since a large number of guards whould attract more attention.
5. Corypheus is way to flashy for such things. He want to hear his victims beg for their lives or ask questions so he can brag about his superiority.