Where in Central Europe are you? I lived in Vienna and now living In Berlin, and while it was a bit of a struggle being vegetarian in the former it think over here there are actually quite a lot of good options (obviously not anywhere near as good as some other places like San Francisco).
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.
Czech Republic. I don't complain about generic vegetarian places (indian food, asian food, some pasta), but if you wanted to go low-carb here, you find nothing.
