Also, is anything east of the Urals (in Russia) considered Siberia? I thought it was only the part in the Arctic Circle.
Colloquially speaking, yes. Although technically speaking it is this:
That is the Siberian Federal District - one of eight federal districts in Russia. The one to the east of Siberia is the 'Far East' Federal District, and 'Far East' is a term I've seen Russia experts instead of Siberia for at least some of that region. Although many parts of the Far East, Sakha included, and also parts of the 'Ural District' (which is the one to the west of Siberia) are considered historically part of Siberia, the federal districts being only recent political creations. Nowt to do with the Arctic circle though, However the Arctic-Pacific drainage basin watershed being used as the border between Siberia and the Far Eastern district.