Learn Swedish: Här är även champagnen väldigt exklusiv. - Here, even the champagne is very exclusive.

Focus particles like även usually sit right next to the word they emphasize. Because the sentence means "even the champagne" rather than "even very exclusive", the particle goes directly before the noun champagnen.

Does placing även before the subject break the V2 (verb-second) rule?

No, it perfectly follows it! The first position is taken by the adverb Här, so the verb är must come second. The focus particle även and the noun champagnen stick together to form a single subject phrase that drops into the spot right after the verb.

Could I use också instead of även here?

You could say också champagnen, but även does a better job of meaning "even" (rather than just "also") in written or slightly formal Swedish. To make the "even" meaning unmistakable in everyday speech, Swedes often use the phrase till och med instead (till och med champagnen).

Why is the adjective exklusiv in its base form without any endings?