Have you ever seen qunari employed by humans as anything other than mercenaries? There is no doubt in my mind that common qunari would not be able to coexist peacefully with humans - the only reason that the Arishok was tolerated in Kirkwall was because he was powerful, politically speaking, and forcing him out would almost certainly be interpreted as an act of war. From a survival perspective, it would make far more sense for any Tal-Vashoth seeking a way out of the Qun to band together and form their own insular community.
Armaas, the Tal-Vashoth merchant who you can hire in Awakening.
I'd disagree that people wouldn't be able to co-exist with common Qunari, as we never get any indication that anyone has a problem with you bringing Armaas back to the Vigil (and if they did, I'd suspect it'd be more because he used to work for the Architect, rather than because he's Qunari).
And while not strictly common Qunari, I'd argue that having the former Tal-Vashoth Maraas being able to find work as a mercenary, as well as Taarbas, an actual follower of a Qun, be able to freely wander around Kirkwall post-Qunari invasion and not be immediately lynched implies that most people in Thedas only really have a problem with Qunari when they are around en-masse, but are able to tolerate individual Qunari more easily.
In regards to Qunlat, I have always thought that it might have been a Conlang created by early Qunari as an easy to learn language for themselves and those they brought into the Qun. Since they had already cast of the shackles of their former society, it wouldn't be too hard to imagine that they might have gone about creating a new language for this new era.
And having a fixed, simple language would certaintly more efficient to learn than try and teach someone an ancient tongue with lots of complicated grammar and rules that can vary, as well as eliminating the possibility that it could end up fracturing into a million different dialects, pidgins and creoles like English for example. Qunlat in Region A would be the same as the Qunlat you'd find spoken in Region B and C, rather than say, the changes in words, spelling, pronounciation and unique quirks native to different regions you'd find in UK English, US English and Jamaican English, just to pick at random.
Personally, I hope that a Qunquisitor will be at least be proficient at swearing in Qunlat, since that's the easiest and most believable part of the language for a Vashoth to learn. Who wouldn't want to tell followers of the Qun to go screw themselves in their own language?