To the america thing - The dragons retreated from Atmora to a place where no humans were. So if the dragons were driven from eurasia America is the most human free region sounds logical.
If youd ask where the dragons could originate in terms of a Skyrim like country / area you could take the following nations into consideration:
Russia, Austria, Switzerland, Canada, Sweden, Tibet. All of these are snowy cold with quite huge mountains. Other countries are either too hot (like the entire US excluding Alaska) or dont have mountains or better not enough.
Other countries would partially be appropiate like Northindia, Southchina, Southgermany, Eastnorway, Northitaly, arguably Westfrance and Westspain.
But in terms of culture i would stuck with either Sweden, Russia, Austria or Switzerland those are the most Skyrim like in landscape and human mindset
Who would win? Well with modern day weaponry dragons dont really have a chance. Since swords work on them we can safely assume that modern weapons work on them in quite a similiar fashion as they would on a crocodile so bullets would work and a machine gun may not cause the biggest holes but should already be enough to stop a dragon. And then we have AAA which would definitely be dragons doom.