No government would claim claim copyright ownership, except in the case that a government had received copyright for a work from some source (e.g. a donation). It is the author of the work who claims ownership.
You will have to figure out the technical details of such file sharing, but the legal details are pretty simple: everybody involved would be liable. Any such data is contained on one of more physical devices, and gets copied to one or more devices. Each act of copying is an infringing act, so if there are copyings to 1,000,000 devices, there are 1,000,000 devices whose owners are liable for copyright infringement.
The person who distribute the software might also be liable, per MGM v. Grokster. Essentially, if a platform is created to enable massive copyright infringement, then the distributors could easily be held liable. Liability would be less likely if the service were a legitimate file-storing system that typically was used legitimately. Since tracking down a million servers is a bit of a task, the software distributors are likely to be the first target.
As for where a person would sue, the issue is not where the infringers are, it is where the protection exists: is the work protected by US law? UK law? Having registered copyright in my book under US law, I would pursue infringers in US courts.
