Yes, that's why I am angrily responding to everyone who criticizes her in this thread. oh wait... 
Perhaps you should refrain from making it personal, then, and focus on the topic of Vivienne instead of the posters?
We know what most of the clans we have experienced do. You have provided one very special case exception that would only account for a clan having one extra mage so I am going to go with the information we do have. Lets also remember that she posed a lot of what she said as questions, she was challenging the PC to come up with a winning argument and the PC failed. Although to be fair the PC can't win, maybe because there is no easy answer.
No, the protagonist didn't fail, because Vivienne wasn't actually trying to learn anything new; she stayed with the same hearsay argument that she started out with, and didn't actually bother to address that the protagonist already tells her that she's wrong to think that every clan behaves in the same way as Minaeve's clan.
Again, you are ignoring context. You could point out many societies in Thedas who "don't have Templars" that really doesn't matter. Vivienne was arguing that measures needed to be taken to police the mages in case of abominations. She was suggesting the use of Templars. The Elf Inquisitors counter point was that their society did not have Templars. So Vivienne points out that they still do take steps to police mages, yes she generalizes with the worst example (I never disputed this) but this example exists and no current Dalish model we know of would work for that situation. The Inquisition cannot adopt a system similar to the Dalish, that's not going to provide the protection she believes there needs to be. So the Inquisitor completely failed to counter her argument, maybe there should have been more response options but Vivienne won that one because she was right despite presenting a slightly unfair argument. Maybe they did that because pro mage characters would just have a complete ideological difference to her and believe that mage freedom was worth the risk they can pose to themselves and others.
Except this example doesn't apply to every single Dalish clan, as the protagonist points out; it only applies to some clans. And it's still not an example that the mages need to be policed when mages are free among the Dalish. If mages are free, then they aren't being policed. Also, Merrill pointed out that the templars are a threat to the clans, and are part of the reason why the clans are nomadic in the first place. If the clan is exiling mages because it puts them in danger due to templars who hunt down the clans (as in the case of Ariane's clan, as she defended her clan from a templar attack), it's hardly an argument that works in Vivienne's favor.
I also don't see why you're acting as though Vivienne was trying to actually debate the issue with the Inquisitor; she acts petulant multiple times, whether it's her snobby attitude towards Blackwall (before the revelation), or her pulling the stunt with the furniture because the Inquisitor had the audacity to have different opinions than she does.
As for the times of the dales, I have no idea how they dealt with the risks so I can't comment.
It was a kingdom with free mages, which is why there were mages among the nobility and within the priesthood (the Keepers of the era).