... In fact, the russian exchange btc-e is one of the top exchanges in the world by volume...
Last I checked it was Bulgarian
No, it is not, don't believe everything you see on the internet. Russian ops, servers around the world, cyprus and bulgaria at one point but it definitely has nothing bulgarian in it.
Is it even registered anywhere? Can't find any info on the site.
No it's not, and they are trying hard to stay under radar. So it will be easier to run with the money later
The fact that they first announced on a russian sub-forum here in pure russian (here: https://bitcointalk.org/index.php?topic=29698.0) points to the origins, though; also the fact that most of their initial fiat I/O methods are only used in Russia/Ukraine.