As large, relatively "hip" capital cities, Berlin and Vienna are probably a "best case". In the German-speaking countries, there does seem to be a growing awareness and interest in vegetarianism, but in small cities in Germany I find my options in restaurants basically limited to pasta and pizza -- and of course falafel -- (though there are enough vegetarians and similar that there are shops selling tofu, vegan cheese, meat substitutes etc.). From what I've heard, the rest of central Europe is even worse.
Yes for sure - the local cuisine is heavy on meat & dairy so you'll have to rely on ethnic and speciality places, which mostly exist in the big metropolitan cities.