There is no "US Copyright Court" per se. Any necessary police action is carried out by the FBI. Litigation is usually handled by the regional US Attorney Generals Office and prosecuted through the nearest US Circuit Court.
The US Supreme Court, located in Washington, D.C.
The US Supreme Court is located in Washington, DC.
A federal court transcript would be a work of the US Government, and would be exempt from copyright protection. Lower court transcripts would be works of state governments, which may or may not be exempt.
Under US laws, all copyright claims under federal copyright must be made in US district court. You would sue for a declaratory judgment that the work did not meet the federal criteria for an enforceable copyright, once you have standing to sue (i.e., someone has threatened to sue you for copyright infringement of an invalid copyright).
According to the Australian Copyright Council: "The Federal Court of Australia, the Federal Magistrates Court and State and Territory courts all have jurisdiction to hear copyright infringement matters. Copyright owners will usually bring an action in the city closest to where they are located and which is most convenient for them. The choice of court may depend on factors including which remedies the copyright owner is seeking (some State courts do not have the power to grant injunctions or award an account of profits)."
Federal Court
The same place where the main us district court for Indian territory was located
US DIstrict Court for the Northern DIstrict of Georgia. Also: The 11th US Circuit Court of Appeals is located in Atlanta as well.
The US Court of Federal Claims. It is located in Wasshington DC.
The US Court of Federal Claims is located at 717 Madison Place, NW, Washington, DC 20005.
The US District Court in California is located in Los Angeles, California. There are several buildings in the area that are all a part of the District Court, but the building located in Los Angeles, is the headquarters.
It varies from country to country. The US Copyright Office is at 101 Independence Ave, SE, Washington, DC 20559, in the Madison Building of the Library of Congress.