Could a song that uses different, but phonetically identical lyrics violate copyright? There is a YouTube video of a song called "Hapi Berth Dey", which the user says is to the tune "Good Morning to You", which is in the public domain. The video never explicitly mentions "Happy Birthday", and says that this song is "about an Egyptian river goddess finding a place to sleep on top of two sheep and a deer named Harrison, who also happens to be governor of Algiers before the French conquest in 1830". Nonetheless, it is phonetically identical to Happy Birthday: Hapi berth dey two ewe, Hapi berth dey two ewe, Hapi berth dey deer Harrison, Hapi berth dey two ewe. The words and the creator's stated intention of what the song is about do not resemble "Happy Birthday", but the lyrics (all of which are real words) are phonetically identical. In other words, they look different on paper, but when sung are the same. Assuming for the sake of argument that "Happy Birthday" was irrefutably protected under copyright law (just the lyrics, since the tune "Good Morning to You" is in the public domain), would "Hapi Berth Dey" or a similar phonetically similar song be in violation of copyright?
It would seem that your song is a derived work. You took the original work and found words that sound the same. If the original work had used different words, your work would have ended up differently. So you have a derived work. Same as making a translation; if the original was different, then the translation would be different, so the translation is a derived work. I was asked "How is this not straight up infringement". But it is. Not only copying is an exclusive right of the copyright holder, but also the creation of derivative works.
The first copyright law dates from 1710, so it's not true that Chekhov wrote before any copyright laws. Any work from prior to 1924 isn't necessarily safe to use (it depends on when the author died). It is in the US but will complicate things if you publish internationally. Unless you translate with something like Google translate, translation is definitely a creative process. This is especially true (although probably not significant legally) for something like a poem, where its' extra hard if you try to keep the original metre and rhyme scheme. If you publish work in the public domain, you would have some claim to the typography. If the translator has done a copyright assignment to the publisher as part of the publishing agreement, they would hold the rights to the translated version.
Copyright never protects ideas or processes, it only protects expression: words, images, and sounds, some of which may describe ideas. But when a work is nothing more than a translation of an idea into words, with no independent originality -- when almost anyone would use more or less the same way to describe the idea, then the work will not be protected by copyright at all, as it is not considered an "original work". Computer code that implements an algorithm often falls under this rule. It is my belief that the code shown in the linked SE thread would fall under this rule, and would not be protected by copyright at all. If this is correct, then anyone may share such a program with no copyright concern.
The commentators are just making stuff up when they say that you can freely infringe on copyright as long as it is for personal use. It is true that "personal infringers" are less likely to suffer the legal consequences of any infringement (partly because it's easier to avoid detection and partly because the hassle to award ratio involved in suing a personal infringer is too high). It's a misunderstanding of "fair use", based on the legally erroneous assumption that anything is okay until you make a business out of it.
A "similar brand", even a "knock off", does not infringe trademark protection (which is the issue here, not copyright) as long as reasonable consumers or purchasers will not be confused or mislead into thinking that the product is the same as the original product, or is made by, affiliated with, sponsored by, or authorized by the makers of the original product, or that the knockoff in some way shares the reputation of the original product. Obviously that is a fact-based judgement, but a name that alludes to another product but is obviously different is generally not considered an infringement. (I recall reading of a case in which the well-known "North Face" clothing brand tried to sue a new brad called "South butt". I believe that North Face lost. Apparently I was wrong and the case was settled.)
I think that both your examples would be considered, if not outright copies, then at the very least derivative works of the originals. Under US law, the copyright holder of a work has the exclusive right to prepare derivative works. So anyone who prepares such a work without the authorization of the copyright holder is infringing their copyright and will be liable for such infringment. The US Copyright Office, in their Circular 14, explicitly includes &quot;a new version of an existing computer program&quot; as an example of a derivative work. That would certainly seem to cover the GTA folks. The concept that derivative works generally include &quot;translations&quot; might capture them, too. Your example of transcribing a musical performance isn't explicitly mentioned, but I think your sheet music would likewise be a derivative work of the performance: it includes all the editorial and arrangement choices made by the orchestra. Of course, both the performance and your transcription are derivative works of the original composition, but since the composition is out of copyright, there's no legal problem with that aspect.
Copyright protection is about certain acts, and not about relationships between products. Copyright law says that the creator of an original work hold the exclusive right to copy and to authorize creation of derivative works. Copyright law does not say that anybody can freely create derivative works as long as they are different to a certain extent. So if you take an original Mario and modify it a teeny bit, that is a violation of copyright; if you take an original Mario and modify it hugely, that is a violation of copyright. Degree of similarity is relevant on some cases when the factual question arises whether the allegedly-infringing work is based on some protected original. This is most obvious in music cases, where all baroque music has some similarity to all other baroque music, all death metal has some similarity to all other death metal, and so on. There is not a legal quasi-statutory standard for measuring substantial similarity in music. The scientific underpinning of such a standard would be based on (weighted) combinatorics and the idea that there are only so many tunes possible (that would be a huge number, until you get to the "within a genre" condition). It seems obvious (by your "admission") that the derived works are based on protected works, so Nintendo's permission is required to legally create such works. However, you do or would hold copyright in your unauthorized derived work. Without a trail of evidence such as a SE question pointing to the connection, the derived images might be hard to connect to the originals. In addition, you may be able to avail yourself of a "fair use" defense, in case you get sued by the original creator. Factors favoring such a defense are the insubstantiality of the copying (a small portion) and the "transformativeness" of your creation.
It is true that any work of the US government is not subject to copyright in the United States; it may be subject to copyright abroad (the relevant law excludes US government works from US copyright protection; other countries have their own copyright laws that generally don't explicitly exclude US government works, and so the works may be copyrighted there). A government work is defined as something produced by a government employee in the course of his official duties. It doesn't include everything released by a government agency; for instance, if a contractor makes something and the contract specifies that the government gets the copyright, the work is copyrighted (since it wasn't made by a government employee). If a foreign cosmonaut or astronaut composes and sings an original song in a livestream, then NASA may not have copyright in the livestream but the foreign astronaut would have copyright in the song. That said, NASA has a page of guidelines for reuse of their media, where they say that their stuff normally isn't copyrighted unless otherwise noted. They don't make any sort of guarantee, but they suggest you'd probably be fine embedding it, at least as far as they're concerned.