Distinctive arrangements are certainly copyrightable, being original work, even if based on previously existing material. Such copyrights don't preclude someone else from creating his own arrangement, as long as that arrangement doesn't directly incorporate the copyrighted distinctive bits which the first arranger added to the base work--and presuming that both arrangers got permission from whomever holds to the copyrights to the original work. That is my understanding of US law, though I'm admittedly not a lawyer and if you solely act on my "legal advice", you're an idjit.

Performance is copyrightable only as a recording--though you have no right to record someone else's performance without permission--, but arrangement and performance are two separate aspects. Musical style as a generic entity is not copyrightable, but an arrangement is musical style applied in a specific way to a specific work, along with other creative aspects. Check most liner notes and you'll see clearly that arrangements are copyrighted--even when they're so derivative the claim may be contestable.

New lyrics are certainly copyrightable, even if they form only a portion of the work overall. Similarly, new melody variants which are substantially different from the original or "known" tunes are copyrightable, as are distinctive bridges and other musical material not present in the original work. The fact these original contributions derive in part from an established work makes little difference. The line between "derivative" and "original contribution" is unfortunately a hazy one that may only be decided rather arbitrarily in court.

Ideas are not copyrightable. I can apply the same basic idea to a work as you, as long as my concrete expression (wording, tune, arrangement) does not infringe on your copyrights.

A difficulty with the Carter copyrights is that they never declared what part of a work they had an actual right to copyright. They just slapped a blanket copyright on the whole damn song. From the legal perspective, as long as a copyright holder can demonstrate that, given the similarities, you've copied from their "original work", your only defense is to show previous or concurrent material proving that those areas of overlap were not added by the Carters. Even if you can show that the Carters had no valid claim to some parts of the work (like the basic lyrics or tune), it doesn't invalidate their potential copyright to the remainder, and it is your responsibility, not the claimants, to prove that your work doesn't infringe on those other areas. It's a messy situation, especially given that, after so many years, few people are living who might testify one way or the other, and written records or recordings that might document how a song had evolved and disseminated after its creation--things that might prove the Carters had made no clearly distinctive contributions--no longer exist or may never have existed. The excessive terms of modern US (etc.) copyrights make this situation even more preposterous.

All that said, it is undoubtedly true that technical copyright infringements are numerous and often flagrant, either from ignorance that such copyrights exist, from ignorance of copyright law, or from deliberate violation (the "do it first, ask permission later" approach). And I believe that for a copyright holder to maintain a copyright, he must demonstrate that he has been reasonably diligent in protecting his copyrights from most previous infringers. Thus, if a work has been allowed to wander around for decades unchallenged as "traditional", or if the Victor company and successors have been lax in pursuing copyright violations, they'll be hard-pressed to win cases of later infringement. Not that they can't bankrupt you in the trying: that's the modern way copyright suits are decided.