We are talking post-Battle of Denerim, specifically.
What does that have to do with this discussion? The event in which the monarch(s) is/are elected is the Landsmeet.
@Jeffry It doesn't matter what it's based on. All that matters is what the canon states about the titles and the process. The codex entries confirm what I wrote.
Fergus becoming Teyrn is as I wrote. If Bryce names him such then it is so. Otherwise the title is in dispute between Fergus and the human noble. With Fergus unable to fulfill the role, the title automatically falls to the human noble. Also, even if you think Fergus automatically gets the title after the battle of Denerim, that doesn't change the fact that they noble held the title during the Landsmeet, which is when the decision of who shall rule is made.
While Origins doesn't confirm which teyrnir Redcliffe is part of, I supposed Inquisition confirms that the monarch has control over it, as that is granted to the mages by the monarch. Although even this is fishy, as I know Anora had to convince the Bannorn to let the mages stay. In any case, a Teyrn is a higher rank than an Arl, which is only slightly above a Bann. Also, Eamon owes you. So, there's that.
In the human noble origin you can talk to someone named Dairren. He confirms that many said Bryce should have been king instead of Cailan. This confirms that a teyrn can be elected king. Also consider the fact that every ruler of Ferelden is elected by the banns. Therefore, the banns can elect anyone they want. And as I already wrote, the Teyrn of Highever is the highest ranking leader in Ferelden after Cailan dies.
As for Alistair and Anora, both of their claims are weak. Alistair is a half-blood prince who does not want to rule. Anora is a consort who was shoved aside instantly after the king's death. She has administrative experience and nothing else. The Teyrn of Highever has survived multiple assassination attempts, commands Ferelden providences, and controls a massive army including aforementioned half-blood prince. The answer is obvious. The Teyrn has the strongest claim, and by Ferelden law he is already Ferelden's de facto leader.
The royal family and any relation to it does nothing but provide claim to the throne. It is not a guarantee to the throne, nor is it the only way to have a claim.
You can't know that the mages would not fight against Loghain's forces if needed. Logically they would, since Loghain caused the tragedy at the Circle and Loghain would have to be stopped before the blight could be stopped. The dwarves and elves? Yeah, they would sit that one out, for sure. But the Teyrn of Highever would still have the Circle and the Ferelden loyalists on his side against Loghain's usurpers.
You seem to be forgetting that Loghain was making a claim for the throne as well through his title as Teyrn of Gwaren. He was the only usurper/dictator there.
That's exactly wrong. Ferelden is an elective monarchy. Every single person to rule Ferelden must be and was elected by the banns. No exceptions.
The next monarch after a joint ruling Cousland and Anora, or just Alistair and/or Anora, would obviously be up to the Bannorn to elect, same as always. But Teyrn Fergus would have the strongest claim, as he would be the highest ranking leader in Ferelden.