"Russia is far."
It’s indeed an adjective. The adjective originally comes from the word Русь 'Ruthenia'.
The adjective «росси́йский» means 'related to the modern country of Russia', while «ру́сский» means 'related to the Slavic people mostly living in Russia'. Russia is a big state, not only Russians live there but also Tatars, Bashkirs, Komi, Buryats, Kalmyks, Yakuts, Chuvashs and many other people live there.
See this discussion for more information: https://www.duolingo.com/comment/11651303
Yes. Compare with «Росси́я зде́сь» 'Russia is here'.
You could use an adjective here: «Росси́я далёкая» or «Росси́я далека́» (short for of the adjective).
«Далеко» is an adverb, «далека» is a short form of the adjective. Both work here. Long form, «Россия далёкая», might work too.