Those are of different language trees and are unrelated, though some researchers have tried to claim that Chinese and other Asiatic languages share a common ancestor with these, it's not widely accepted and nearly impossible to prove.
Old World likely referring to Europe. Except they had to include Middle East and South Asia, because it's the same language tree.
Notably there's no Georgian, because it's also it's own language tree but is not in Europe. But the Caucasus is part of the old world. And Georgia is a candidate country for the EU.
Sure but it also seems a bit, I dunno, silly. Sure, you could do a whole forest if you wanted to, and the name 'old world languages' is kinda dumb, as this is just two language families - but it's still a neat visualisation. It's not some conspiracy.
yea depending on how nitpicky you wanna get you can even point out that some language families are intercontinental between eurasia and the americas (not talking about colonialization, theres some related siberian and canadian languages iirc), but its pretty clear that this is supposed to be a general overview and pie languages do well enough for that