I agree that the justification for the other origins seems weak, and it is likely because of their addition later on into the game's development. We see that at least the Cadash choices have ties to the Carta; while our Adaar choices are always hired as bodyguards...although one would think each party would individually bring their own guards, I can see justification for this, if you consider that the Chantry likely wanted a neutral party to moderate it. Although I'm not sure why you'd bring your Vashoth mage with you to a meeting that could very well result in the reformation of the Circles - not to mention the summit is being chaired by the Chantry.
Actually , the mercenaries make a lot of sense when you remember that the Chantry is currently shorthanded after the defection of many Templars and Mages. Those Vasoth mercenaries aren't loyal to any country, so that's even better. As for the Qunari mage, I wouldn't worry; the conclave will have a lot of mages present, so it's not as if some party is going to start imprisoning mages right away.
With the elven origin, I do take a bit of issue with it, but I think it makes a bit more sense than at first glance. One of the major reasons for Dalish clans remaining nomadic is that Templars can and will hunt them down for their mages. With the news of a summit for the Mage-Templar War - which has the potential to have affected clan mobility - it could be speculated that Keeper Lavellan wanted to ensure that she knew what the outcome would entail. If the Circles were to be restored and Templars once again taking up the mantle as enforcers, then it would be important information that she could then pass to other clans. Vice-versa, continuation of the conflict if peace couldn't be made would be potentially damaging to the clans, or if mages were somehow allotted more freedom (although I don't know how, if the summit is being chaired by the Chantry) and Templars done away with, clans would have less to worry about. The outcome could certainly affect the Dalish, so I believe that's why Keeper Lavellan likely sent one of her own. There's supposed to be an Arlathvhen approaching, so I believe this is intelligence the Keeper would likely want in order to share it with the other clans.
I agree with those points. Also, in another thread someone suggested that the Mage-Templar War might have caused a very noticeable increase in the number of elven mages fleeing to Dalish clans. With the dangerous possibility of rebel Templars going after them and bringing problems to the Dalish. So there's an interest and there's a need.
The question is: why the Lavellan Clan? Why a lone clan in the Free Marches with little to no contact with humans, and by the personal decision of their Keeper? What motivated her more than other Keepers from clans that should live nearer the meeting place?
How they get in to the summit is another story - I doubt the Divine would have invited the Dalish. A mage could pose just as that, but I have no clue how a rogue or a warrior would. I still have a difficult time justifying why she would send her First, though. Why would you send your successor on a potentially dangerous task all the way in the Frostbacks?
I think it's a matter of value versus effectiveness. A First is very valuable. It's a mage and those are rare. Maybe the clan has more than one mage, like Zathrian's clan, so the Keeper can always train another one, but it's a waste. However, the First is also the one with the best education after the Keeper herself. He or she should understand much better what's being discussed in the conclave, including the possible ramifications, than a hunter, no matter how skilled they are. On the other hand, a hunter is trained for survival, so they have more chances to survive the mission.
Oh, and let's not overlook the importance of losing one of the best hunters in a nomadic society. It would be like losing a good deal of fertile lands for a kingdom.
Of course, we are playing those characters, so our hunter will understand very well what he or she hears and our First will always survive no matter how dangerous the trip may be. But that's metagaming.