What would your Dalish Inquisitor prefer?

None of my Dalish characters so far were warmongers, so none of them would start a war, maybe use your influence to get the different elven fractions on one table and form an alliance (including Briala and her spy network perhaps). See, that you have a good standing with the new divine and try to negotiate land from the humans - not the most realistic approach and it may take a long time, but it could be doable, especially in a world stat like mine, where Dalish were the HoF and the inquisitor and Dalish Clans helped defending human settlements (Lanayas Clan in Denerim and Clan Lavellan in Wycombe) - it could be the beginning of change. The inquisitor has most likely gain a few favors, perhaps even from the emppress of Orlais herself, if saved and the king of Ferelden, if you help him with the problems in the castle (I don't know, if Anora has a similar mission, so far I had only Alistair and Anora as a couple).
And on a more practically note: if you have a military power behind you, people are more inclined to negotiations, I guess

Oh... Answer varies from one Quizzy to another. My big-hearted Champion would try to achieve things peacefully. Preferably by showing Dalish are someone you want as allies and that giving them their land would ensure their support when needed. Knight-Enchanter, "calm before the storm" type, would try peaceful path, but wouldn't hesitate to use force, especially if she saw interest of her people was in (even more) danger. And of course there's Assassin lady who would happily use "the Left Hand of the Divine"-type of actions to have her way. All while wearing that innocent smile of hers.

Hard to say. I think several would want to just go to war, but i'm sure most of them are smart enough to not just attack what is essentially the seat of Andrastian power. If one was to attack Orlais, especially by the Dalish who are not only elves but Creator worshipers, then it is very likely that more than one nation will get involved to crush what they see as a heretical and unjust conquering.

But most Dalish clans I know would not view 'peaceful' means of acquiring homelands to be viable either. It doesn't matter how nice you are, people will still find a reason why they should remain in their second class citizenship.

Most likely they will take an "attack from within" approach when 'attacking' the Orlesian Empire. But it would require the City Elves to play a part by rebelling, refusing to work in the upper quarters or accepting Orlesian authority. Most nations become exceptionally weak when their social structure is compromised---if not by eradicating the ruling class, then by the unrest in the lower class. I imagine there would be something of a labor shortage in Orlais if all of sudden their #1 source of cheap labor simply refused to work. Sure they could just hire commoner humans, but I can guarantee you they would want more pay than their elven predecessors. And all the while the elves would likely be corralled into a tighter and tighter space, boiling in their rage, until one day it just erupts into violence. The ones corralled in the alienages would want to rebel, and the ones in noble houses would want to betray. If the Dalish/City Elves play their hands right, they can collapse the Orlesian Empire by essentially starting a Civil War. National powers can't get involved in that--not without appearing to take advantage of Orlais's weakness for their own gain. Assuming no other nation comes in to conquer the weakened empire, the elves would have the opportunity to defeat Orlais by using their own people against them.

Not too unlike what happened with the Elvhen Empire, Old Tevinter Imperium and the Circles actually. But the trick is making sure that they are still standing once all is said and done. They would have to organize quickly enough to not only claim the Dales, but protect their position as other nations try to make the most of a weakened Orlais and try to take advantage. Then they have to have the Dales be recognized as a sovereign nation by other national powers. If they can somehow manage that, then odds are my quizzy would not only condone it, but support it. Likely using their title as the Herald of Andraste/Inquisitor to speed the legitimizing process.

We're talking about a hypothetical scenario where the Dalish have the necessary military power. Then you may tell us what your Dalish Inquisitor would want and talk about the clans in general as well.

I would start by pointing out that at the end of the main game my Dalish Inquisitor had armies at his disposal that could challenge nations and yet that didn't stop them shutting down the Inquisition, so just because you have the theoretical fire power to wage a war doesn't necessarily mean it is going to be successful if you do.

It also depends at what point we were going to launch this campaign. The best time would have been at the end of the main game, when the Inquisition was at the height of its power and so could back up any move by the Dalish. Briala was in control of Orlais, so I'd have just ceded Suledin Fortress to the Dalish as somewhere that is fairly remote from the main cities in the northern Dales and easy to defend up there in the highlands. Would also come to an arrangement with Fairbanks in the Emerald Graves and also suggest to the Dalish that they take over the Arbor Wilds now that Abelas and his sentinels have abandoned it. That would give the elves a sizeable area for their homeland without it severely impacting on the nobility in Verchiel, Lydes and Halamshiral. With any luck we could also get back the Exalted Plains too, considering that anyone who lived in the villages there was either killed during the civil war or appear to have abandoned the place.

I would suggest to the Dalish that they allow any human peasants still living in the areas to remain as they really aren't the problem and we know that there was a fair bit of resentment against the nobility among the ordinary people of the Dales, so they would probably back the Dalish against aggression on the part of the nobles. Then just concentrate on building up our defences against the time when Briala is no longer in charge and the Chevaliers have recovered sufficiently from their inane civil war. Also continue to build up good relations with the Avvar, so we don't have to worry about our rear.

If we did that then I think there is no reason why we couldn't hold the Dales in the future. Back in the time of the original Dales, the elves were more than a match for the Orlesians on their own ground. It is only when they overstretched themselves by actually venturing deep into enemy territory to attack Val Royeaux that things started to go wrong.   In this scenario Leliana is the Divine and pro-elves so she would probably dissuade any direct attack against us provided we didn't do anything provocative.  I'd forget about taking back Halamshiral.   Most of the elves there were killed by Celene and it would only have bad memories for those that survived.   Suledin Fortress could be the basis of our new Halamshiral.

If our campaign was not due to start until after Trespasser, then the situation would be somewhat different considering the Inquisitor would no longer be able to back them up and the Orlesians would appear to have been repopulating he abandoned areas. In that case, I suggest to my Dalish army to do what I have done in my fan fiction - march north and take back Arlathan Forest whilst Tevinter is otherwise engaged battling the Qun. To be honest, I'd much rather have a homeland further north. Despite appearances in the Arbor Wilds it must be bitterly cold in winter and the Emprise du Lion and the Emerald Graves would probably be not much better. The climate in Arlathan Forest would be much more pleasant and its situation a long way from the seat of the Chantry would be an advantage. By the time Tevinter and the Qun had stopped clobbering one another, again we could have built up our defences sufficiently to repel all invaders. Would probably be fairly easy to remain isolated if that is the wish but it would probably be advantageous to foster good relations with Rivain, owing to their unorthodox views on magic and religion.