Assuming you're American, I believe you can get a Schengen visa for most of Europe from any number of countries, including Britain (if you hurry, and it may not be called Schengen since they aren't a member). So try shopping around – it's usually easy if you have ancestors from a country and every country has additional programs for certain purposes (being jewish, for example, gets you German citizenship with no further questions asked).

A Schengen visa allows you to travel freely in the EU, but not to live anywhere unless you actually have a long-term visa for the place.

All administrative acts will require you to have a long-term visa in the country you are doing them.