Copyright on a physical object where no patent exists Lets say my company make a new shape of Rubik's Cube (a round ball twisty puzzle) and we call it a "Ball Cube" (my company is called "Puzzles" so its a "Puzzles Ball Cube"). I patent the "Ball Cube" and start selling it... 20 years later the patent expires and lots of other twisty puzzle manufacturers create the "Ball Cube" and call it their own brand so lets just say "Rubik's Ball Cube" and "LanLan Ball Cube" and "China Ball Cube". Are they free to do so? do i legally own copyright for the "Ball Cube" phrase or the design of the original? Or would I have to file for a trademark? Can a physical object like this twitsy ball cube be protected under copyright after the aptent expires?
You would want to establish trademark protection on the phrase "Ball Cube": copyright is not generally a good way to protect names or other short phrases. See, for example, Can I copyright the name of my band? from the U. S. Copyright Office, which notes that "names are not protected by copyright law." Furthermore, you're interested in preventing others from selling a similar object using a similar name, and that's precisely what trademark protection is for. The ball cube design would potentially be eligible for copyright protection, but you should be aware that this protection would not extend to elements of its design that originated in Rubik's Cube, because your design would be a derivative work.
Alice has been developing her own enhancements, and they're pretty similar to Bob's. Neither Alice nor Bob has copied the other's enhancements, so neither has violated the other's copyright in the enhancements. Whether that could be proved in court is another matter, of course, but since the original work is licensed under creative commons the question unlikely to arise in court. Would Alice be prevented from coming up with enhancements to her own game if other people could prove they thought of and released the idea first? No. Copyright does not protect ideas. It only protects a particular expression of those ideas from being copied. Theoretically, if two authors come up with identical 500-word descriptions of something and can establish that each did so independently, neither has a claim against the other. The practical problem there, of course, is that it would be impossible to prove such a thing. Could Alice outright claim Bob's "Adapted Material" because he developed it on her original work? Assuming that in publishing his adaptations Bob followed the terms of the creative commons license with respect to the original work, Alice's only claim would be that he copied her adaptations without following the terms of the license. If Bob can show that he did not do so, her claim would fail. In a comment, you wrote: Suppose Alice went ahead and intentionally, somehow provably ripped off Bob's "Adapted Material" because she liked the content so much, does Bob reserve any rights on his adaptation, or is Alice able to commercialize the work that Bob did in extending her original work? If we assume that Bob complied with the license of the original material, we know that he licensed his adaptations under "the identical terms," so Alice would be able to use Bob's adaptations under those terms for non-commercial purposes. Since the assumption here is that Alice provably copied something of Bob's, I think it is fairly clear that she would be liable for damages if she exploited that material commercially without paying royalties.
Can I sell below parody T-Shirts? Sure, you can sell those shirts. But there is no guarantee that your own determination and claim of Fair Use for a parody would prevail in court. The determination that your use of those derivative designs - Fair Use as a Parody - is not yours to make; it is for a court to make, if and when the copyright holders of those two franchises choose to take you to court. Your determination of Fair Use could only be valid in the US; there may be no Fair Use law in your country, and any relevant international laws and agreements will impact what the legal steps the copyright holders can take against you. Read Fair Use again for exceptions to the law and about international laws such as as Berne Convention and World Intellectual Property Organization. Warner Brothers (Superman) and Paramount (Godfather) could decide at any time to confront you with a cease and desist letter or a lawsuit to challenge your claim of Fair Use. They may win; you may win your defense of their lawsuit. That's a risk you will take. The fact that other people currently produce shirts with similar designs doesn't mean anything. They may not have been confronted by the copyright holders; or the copyright holders may not care to confront small producers of possibly infringing designs and products.
I'm assuming that you are in the UK, as you are talking about the British Standards Institue. In general the truth cannot be copyrighted but an expression of that truth can be, provided that it is creative or original to at least some extent. In this case the equations and constants you want to use are descriptions of scientific truths. If you translate them into another form (e.g. a computer program) then you are not copying the creative bit (the layout and arrangement of those equations and explanatory text), so you are not violating the copyright. Edit: I should also have said for (3) that their descriptions of the constants and variables will be copyright. You would have to avoid copying their words. However given that these are going to be terse descriptions of facts your words can still be pretty similar without infringing on copyright, because there are only so many ways of describing the acceleration due to gravity, or whatever. Take a look at some alternative references to see what words they use.
I'm not sure about USA law, it's probably similar to UK law. In the UK a trademark is registered for a particular business activity, and you can't just blanket register for "all" activities as that would be anti-competitive. I have a trademark "Dreamcraft" for dream interpretation and related activities. However, the name "Dreamcraft" is also a registered trademark for a company selling luxury yachts, and again for a company selling up-market craft materials. A website or organisation that is a gripe-site using the same name would not be in breach of any of these trademarks because it wouldn't be in direct competition with any of these companies.
If you have a truly novel and non-obvious game idea, you could patent it, and that would cost many tens of thousands of dollars if not hundreds of thousands of dollars (U.S.) in legal fees, etc. and probably a couple of years of patent prosecution, if your idea has not already entered the public domain through public display or sale. Most ideas for games are either not novel, or would be obvious to a person skilled in designing games. But, if your idea is really and truly new, you could do it.
The basic principle about copyright protection is that the expression of an idea is protected, but the idea itself is not. So wholesale copying without permission is infringing. But the abstract algorithm is not protected by copyright (and let us assume that it also isn't patented). By way of analog, an insertion sort is a pretty easy concept to grasp, and once you understand it, you can re-create it, independent of how the original example (where from you learned about the sort) is expressed. So the question is whether it is necessary for you to copy that code (copyright protects against copying), or can you independently re-express the algorithmic idea (ideas are not protected)?
A character can not be copyrighted. Only a work (picture, text, movie etc.) featuring that character can. However, a character can be registred as a trademark (more specifically, its name and its appearance).