You might be interested in some information on the
Witanagemot. It's the IRL Landsmeet, and modern scholars (according to Wikipedia; I haven't done any personal research into it) aren't certain exactly what it could or couldn't do. Of particular relevance:
These documents clearly indicate that the witan was composed of the nation's highest echelon of both ecclesiastical and secular officers. Present on the ecclesiastical side were archbishops, bishops, and abbots, and occasionally also abbesses and priests; on the secular side ealdormen (or eorls in the latter centuries) and thegns. Members of the royal family were also present, and the king presided over the entire body.
Just like the Landsmeet.
The king alone raised a man to the position of a gesith, a thane, a provincial or local reeve, a court officer or a royal chaplain, one of which titles seems to have been the indispensable qualification for a vote. .. as no periodicity of the assembly was fixed, the king determined when and where it was to meet, for the most part choosing places under his immediate control; he presided, spoke first, put his questions, proposed his bills, and finally dismissed the witan.
Unlike the Landsmeet, which a noble of sufficiently high rank (an arl) can call.
The witan was noted by contemporary sources as having the singular power to ceosan to cyninge, 'to choose the king' from amongst the (extended) royal family. Nevertheless, at least until the 11th century, royal succession generally followed the "ordinary system of primogeniture." Chadwick interpreted these facts as proof that the so-called election of the king by the witan merely amounted to formal recognition of the deceased king's natural successor.[13] But Liebermann was generally less willing than Chadwick to see the witan's significance as buried under the weight of the royal prerogative... Liebermann's more subtle position seems to be vindicated by testimony from abbot Ælfric of Eynsham, the leading homilist of the late 10th century, who wrote: "No man can make himself king, but the people has the choice to choose as king whom they please; but after he is consecrated as king, he then has dominion over the people, and they cannot shake his yoke off their necks."
And here's the scholars debating over one half of your question: Could the Witan/Landsmeet pick a king from somewhere other than the royal line?
In addition to having a role in the 'election' of English Kings, it is often held that the witenagemots had the power to depose an unpopular king. However, there are only two occasions where this probably happened, in 757 and 774 with the depositions of kings Sigeberht of Wessex and Alhred of Northumbria respectively. The witan's powers are illustrated by the following event. In the year 1013 King Æthelred II fled the country from Sweyn Forkbeard, who then had the witan proclaim him king. Within a few weeks, however, Sweyn died and Æthelred was called back to England by the witan. According to the Anglo-Saxon Chronicle, the witan would only receive him back under the condition that he promise to rule better than he had.
A little ambiguous, IMO, because really - was he going to say anything other than, "I so swear"? But it does appear, in theory, that the Witan could legally shut the door on the ruler and (one assumes) select another.
I know, I know: Thedas isn't our world. However, I think when you use our world as obvious inspiration for detailed world design, it isn't unreasonable for those seeking to develop it further (or understand it as-built) to look back at that original source for evidence. Your mileage may vary.
Double-plus however: I don't think it matters. It doesn't matter what the Landsmeet said, or whether they were technically able to say it or not. Ferelden is a nation where wars have been fought over
an apple tree. At the end of the day, what matters is having the power to enforce your will on the country. (I mean, the Orlesians ruled for 80 years and got nobles like Tarleton Howe to swear fealty, and they sure weren't of the blood of Calenhad.)
Anyhow to your questions:
1) The Landsmeet nearly put Bryce Cousland on the throne over Cailan, so I'm thinking yes, they can do that. It's not like Ferelden has a constitution where it's spelled out that only a Theirin can sit on the throne. Calenhad brought the bannorn together by strength of personality and arms, but a lot of the noble families have a mythology of how they
chose to serve under his banner (even if he had to kick their butts first, like the Couslands). They can decide to
chose to serve someone else if they want to.
2) Interestingly, the 9:30 Dragon Landsmeet never votes on the crown. After the Loghain duel is resolved, Arl Eamon unilaterally tells the Warden to pick a potentate. However, this is probably for smooth, quick narrative, so let's pretend that what really happens is that the Warden puts forward a Throne Solution and the Landsmeet approves it...
...but when you are looking for the devil in the details, you can't hide the details. What exactly would the Landsmeet approve? Would Anora start a debate/fight if he said, "I'll marry her and be king"? Would the Landsmeet approve anyway? Would there be a week of political bickering while it was ironed out? Probably.
But that's all a round-up to a big "doesn't matter." Loghain didn't need 'the will of the Landsmeet' to rule for a year. If the Warden is made Prince-Consort, but has the power to rule like a king, he's the king. The
consequences of that might be bad for Ferelden, because Anora will fight it. How hard the Warden pushes the issue, and at what point in their reign, may make a lot of difference there.
Last consideration: what stands in the way of a sunshine-and-rainbows ending with king and queen co-ruling happily, sharing power and trust, is
everyone else. I think that even if Anora came to trust m!Cousland not to shove her off the throne at the first opportunity, were he co-regent, she would be concerned that as soon as he were crowned, everyone would assume he was "really" in charge and stop acknowledging her as the
other ruler. She had enough of that disrespect for her ability under Cailan, and might not want to make Cousland a co-regent for that reason alone.