Can I use any library I want in a public domain program? If I install a library on my system (let's say it's called libfoo and it is under the BSD license), then include the header in my program (in the public domain) and link the program to libfoo, is that legal? It seems like it would be, since no library code is actually getting included in my final binary.
You need to check what license the library comes with. The fact that you want to create a public domain program doesn't give you any rights to any library. So read the BSD license and see what it tells you whether and how you can use the library. For example, if you used a GPL-licensed library, you could not put your program in the public domain legally.
No. Copyright does not have exemptions for obsolete works, use with credit, or non-commercial use. Depending on the purpose for the distribution, this could be fair use, but it is unlikely that a court will consider this fair use when the only reason is for other people to be able to play games. Perhaps you could try contacting Adobe; it's possible that they will give you a license to distribute the Flash Player. This isn't directly relevant to the legal aspect of copying Adobe's Flash Play, but to answer the underlying issue of legally playing Flash games, perhaps you/others could try Gnash, a libre reimplementation of Flash. I have not used it, but apparently Gnash can run some Flash software without using Adobe's player.
It's not fair use. Fair use is when you do something that normally only the copyright holder can do. Playing a video game is the ordinary, intended use of the work. In the United States, ordinary use is not protected by copyright. 17 USC 106 sets out the rights protected by copyright. The include copying the work, producing derivative works, distributing the work, and so on. None of these are ordinary use. Someone could perhaps argue that you are creating a derivative work. I doubt that argument would work because you are not taking any protectable elements from the work. But if anyone did argue that, it would make sense to also argue that if that's so, your use would still be covered under fair use because it's transformative, does not substitute for the original work in any way, and takes very little of the work.
In Germany, there is no concept that corresponds directly to public domain. You automatically hold the Urheberrecht (~ copyright) for all creative works that you make, and it can't be given up or transferred (§29 UrhG). The work only enters the Gemeinfreiheit (~public domain) 70 years after your death. You can however license Verwertungsrechte (economic usage rights). When you make creative works in the course of employment (see §43 UrhG), your employer automatically gets the Verwertungsrechte necessary in the context for the work, which is typically an exclusive right (no one else, not even you, can use the work). Your are not in an employment relationship with your school, so it has no rights to your works and cannot prevent you from publishing them on copyright grounds. When you see advice on the internet to check with your school first, that is U.S.-specific advice. Since you're still a minor (7–17), you only have limited capacity to enter contracts or legal transactions (bedingte Geschäftsfähigkeit). While you are able to make transactions involving your own means (e.g. buying something with your pocket money) or make transactions that are only to your benefit (such as accepting a gift), other transactions are schwebend unwirksam (~ pending ratification), until your parents agree. The relevant law is in §107 and §108 BGB. This is a problem with open source licenses. If you publish software under a license, this license is schwebend unwirksam. Someone might start using the software under the license. But then if your parents refuse ratification, the license would be invalid, and everyone would have to stop using your software and destroy any derivative works they made. This is a bit of a problem, especially since open source licenses are otherwise assumed to be irrevocable. So if you want to offer a license (including open source licenses), please give legal certainty to the recipients of the license and ask your parents for their consent first, possibly even in writing. Per §107 BGB, the license you offer with their consent will be valid.
Generally, no, this will not violate copyright. Your end user might violate copyright, but that is their problem not yours. Your program is a tool, just like a word processor is. If I copy a Harry Potter book into a word processor that does not make the word processor maker liable. There is a concept of "contributory infringement", which I think is what you are concerned about. I don't know about Danish law in particular, but most countries would require evidence that you had reasonable knowledge that actual copyright violation was occuring, rather than just being aware that it might happen in theory. This is normally applied to file sharing services who have to have "notice and takedown" measures, file filters and the like. This isn't your concern as you never have any access to the files created by your users. You can also be found liable if you induce anyone to commit copyright violations. Don't draw your customers attention to the custom monster feature as a workaround for those copyrighted monsters, as that could be considered to be inducement. Also don't provide any "wizards" or similar tools which make it noticeably easier to duplicate the custom monsters (e.g. if you notice that the copyrighted custom dragon stats are all on a linear scale with dragon size, don't create a "dragon creation wizard" embodying that fact.) This assumes that your program runs entirely on the end user computer. Its different if you provide any kind of cloud storage for generated characters.
Is an article licensed under an Open Access license equivalent to a public domain work? No. Intellectual property practitioners and professors often describe copyright as "a bundle of sticks." This means that intellectual property laws grant the creator of a copyrightable work a large number of rights, and the creator can grant or deny others each of those rights individually. So, for instance, an author can grant a publisher the right to publish his or her book in one country, but not in another, or to copy it verbatim but not to alter it. The purpose of a license, any license, is to specify which of those rights pass to the licensee (the end user) and which stay with the licensor (the creator). This is true of creative commons just as it is for any other license. For example, many open access publishers publish under the Creative Commons CC-BY journal. This is an attribution license; it requires as a term of the license that you give credit to the original creator. This is something you would not have to do with a public domain work. In addition, under CC-BY, you have to include a copy of the license with each copy you distribute, and you cannot add your own copy protection to any copies you distribute. Again, these sort of restrictions do not apply to a public domain work. In short: the purpose of a license--any license--is to define the ways in which you can, or can not, use the licensed materials. Any license that contains any provisions restricting the licensee's use is going to be more restrictive, by definition, than the use of something in the public domain.
Your understanding of the GPL is a bit off. GPLed code doesn't generally force you to GPL the output of the program, but that's just because the output of the program is normally not a derivative work of the program. For instance, if you write a novel in Emacs, your novel is an entirely original work. The fact that you used Emacs as a tool doesn't mean that your novel is somehow based on Emacs. This generator is different. It generates sprites by putting together art assets made by the program's creator. That means that the output contains a substantial amount of content made by the program creator, which means that it would likely be covered by the program creator's copyright. If the content was licensed to you under the GPL, you normally have to abide by GPL restrictions when you redistribute the content or incorporate it into your own program. Copyright holders can, if they want, grant additional permissions to their content and allow you to incorporate that content into nonfree software. For instance, the GCC compilers have an additional permission for their runtime libraries to let you use them in any GCC-compiled code; without that permission, GCC could only be used to compile GPL-compatible code. But unless the copyright holder has granted those permissions, when program output contains large amounts of their copyrighted content you're bound by the GPL when using it. In this case, the program specifically says that the art is dual-licensed under GPLv3 and CC-BY-SA-3.0. Since the generator's output is a combination of premade art assets (the buttons just let you tell the program which art assets to combine), the output is a derivative work of those assets. You can't use it unless your use is compatible with the GPL v3 or CC-BY-SA-3.0 (either works, since dual licensing lets you pick either license).
"Public domain" refers to things in principle copyrightable but where protection has lapsed, been repudiated, or is a statutory exception (such as government works). A website is not "in the public domain". The idea that a website is "public property" is (*cough*) mistaken. There are basically two ways in which a web interaction could be illegal. The first regards whether accessing another person's computer is illegally accessing a computer, which is a crime. Authorization essentially comes down to "permission": if the owner permits me to access the computer, I am authorized. Putting stuff out there on a web server is an open-ended grant of permission to look at a web page. That simply means that if I create a web page (with a bunch of links or not), I am granting you permission to interact with my computer to that extent. It does not create permission to hack into a password-protected subdirectory. An ordinary web crawler automates what a clicking human does. Copyright law is also relevant, in that the stuff I put on my webpage is not to be copied without permission. Any webpage access necessarily involves automatic copying from machine to machine: in putting stuff out there for the world to see, I am saying that the world can do that level of automatic copying that arises from normal html-and-click interactions. It does not mean that you can download and do stuff with my copyrighted content (i.e., it is not an abandonment of copyright: I did not put that stuff in the public domain). Putting a web page out there in an unrestricted fashion means that you've given a certain level of permission to "copy" (at least in the automatic server-to-browser viewing sense). I may want to impose conditions on peoples' access to my stuff, so I can impose terms on such material. For instance, I may require users to agree to certain conditions before accessing the CoolStuff subdirectory. Users then have to jump through a minor hoop and agree to those terms. In that case, my permission is conditional, and if you violate the terms of that agreement, I may be able to sue you for copyright infringement. It could then be a violation of my terms of service (TOS) if I say "you may not crawl my website" (in less vague language). A TOS gets its legal power from copyright law, because every webpage interaction involves copying (I assume that technical point is obvious), and copying can only be done with permission. You may technologically overcome my weak click-through technology so that the bot just says "sure whatever" and proceeds to illegally use my web page: I can sue you now for copyright infringement. The robot-specific methods of meta-tags and robots.txt have no legal force. Although there is a way to say "no you may not," which is tailored to automated access, the meaning and enforcement of these devices has not yet reached the law. If my page uses NOFOLLOW and your program doesn't know or care, you (your program) do not (yet) have a duty to understand, detect and respect that tag. Prior registration is also not a legal requirement, and very many pages that are on the master crawl list get there from being linked to by someone else's web page. Again, there is at present no legal requirement of pre-registration (and there is no effective mechanism for verifying that the site owner has registered the site). Archiving and especially re-displaying someone's content is, on the other hand, not legal. It would be plainly copyright infringement if you were to scoop up someone else's webpage and host it. You can analyze their material and somehow associate it with some search terms, and display a link to that page, but you cannot copy and republish their material. You can put very short snippets out there taken from a web page, under the "fair use" doctrine, but you can't wholesale republish a webpage. (It should be noted that the archive.org is an internationally recognized library, and libraries have extra statutory powers to archive).