what differentiates Poles from the other nations of the world?
Poland has her own culture, language, and territory.
Why does Poland exist?
Because it has her own culture, language, and territory, as do most nations in the world.
What is its mission/purpose, if any?
To maintain her sovereignty and independence, which is the right of other nations in the world.
Polish is special due to the incidents of let's say last 250 years.
Poland's history was definitely turbulent yes, however I would beg to differ. Most of Eastern Europe was going through very similar troubles, aside from them all existing under serfdom.