How illegal would it be to use fictional locations, companies, etc. from a video game in a different video game? Let's say I wanted to create a knock-off GTA-esqe game. If I wanted to use locations like Los Santos, San Andreas, Blaine County, Paleto Bay, etc. would there be any IP concerns? If I wanted to use fictional company names (such as Merryweather Security or Liveinvader), would there be any IP concerns? If I wanted to use vehicle makes/models/etc. from the GTA universe, would there be any IP concerns? Would these concerns change if it was a criminal story-based game (like GTA is) or if it was a story based game (maybe from a Law Enforcement perspective) or if it was solely open world?
It's hard to give a definitive answer, since the specific details matter. You should read this question and answer, What is a derivate work? for more information. If you're really considering investing the time and energy to create such a product, you might consider getting advice from an actual attorney, and not from strangers on the Internet.
Under United States law, it is not illegal to simply make an account on a forum where criminal activity takes place. The closest thing I can think of would be misprision of felony (AKA failure to report a crime), which requires active concealment (see United States v. Johnson, 546 F.2d 1225 (5th Cir. 1977)). Simply observing evidence of criminal activity and not reporting it would not qualify. However, if that forum also contains material that is illegal to posses (such as child sexual abuse material), downloading that (even by simply viewing it using your browser) could be a crime. I would note that I am specifically not advising you whether or not doing any of the other things, like making and publishing tutorial videos on how to access such sites, is likely to get you into trouble with the law. If you want that sort of legal advice, you should contact a lawyer, as the advice is going to be very specific to the exact details.
It's almost certainly violating the company's rules, and yes, you can get into trouble for that (in the sense of an internal disciplinary matter). Whether it's a criminal hacking will depend on a) what you did; b) where you are ... but I wouldn't rule that possibility out.
A company does not cease to exist simply because it goes bankrupt. The company may wind down its operations, but it may just go through a process of restructuring its debts. If the company is merely restructuring, the bankruptcy would not probably not have much effect on its ownership of intellectual property such as copyright and trademark rights. So it would retain those interests in the video game, and the company making the sequel would need to obtain licenses from the original company. If the original company is going through bankruptcy in anticipation of shutting down completely, you can expect it to sell off all its assets, which would include its copyright and trademark interests in the game. In that case, the company making the sequel could either attempt to purchase those rights itself, or it would need to obtain a license from whoever does buy those rights.
Not only can’t you trademark it, you can’t use it The original logo is covered by copyright which belongs, prima facie, to the original artist. It doesn’t matter that they are based in Russia; Russia and the US are both signatories to the Berne Convention which means they protect each other’s copyright. That means you can only use it if it is fair use (it isn’t) or if you have the copyright owner’s permission (you don’t). Could I still use the logo I bought and trademark it in the US granted that the seller had made some revisions to the stock photo he found? Not if the seller didn’t have permission to make those changes. Creation of a derivative work is one of the exclusive rights copyright gives. The seller had changed up some parts of the stock image, this includes color scheme, orientation, and made the picture look a little low poly. See above. The original artist of the stock photo is based in Russia and as far as I can see there is no registered copyright on it and don't think they could apply for US copyright anyway. They already have copyright. They would need to register it in the US before they could sue but there is no impediment to them doing so. While I'm not sure where the seller (located in Pakistan) officially downloaded the logo, I had nothing to do with the final design of it or downloaded anything from a stock photo website myself, so I'm not sure if I'd be bounded by any terms of the stock photo website Makes no difference. Just because you didn’t steal the car, that doesn’t make it ok for you to drive it. The stock image is very niche and a bit random. Across all the websites the artist has published it on, it has about 5 or 6 downloads altogether. Not relevant at all. As far the copyright of the seller's work goes, the Fiverr terms state that buyers have all the copyright, though I don't know if this is nullified by the use of the stock image. You can’t sell something you don’t own. If the seller had no right to upload the photo (as it seems they didn’t), the terms of the website don’t matter. The true owner never agreed to those terms and isn’t bound by them.
Yes you can. The pieces of information you are going to include are facts. Facts are not copyrightable. The names will be trademarks but you will not be pretending to have any connection with them, so just using them for reference is fine.
Names of people, institutions, and events are not protected by copyright. Things that have occurred at events like math tournaments are facts, and may be recounted, in your own words, with no fear of infringing any copyright. Facts are never protected by copyright, although a particular description of facts could be, and so could a particular selection and arrangement of facts. Specific math techniques and their names are not protected either, and may be described without infringing copyright. The items you mention in the question are: video game / movie references and names No copyright issue here. common integration bee problems No copyright issue here. names of a university / math competition organizers No copyright issue here. integration techniques and formulas No copyright issue here, unless you copy an extensive description of a technique without rewriting it in your mown words.. using someone's Overleaf Latex package to format the book This depends on the license for the package, but there is not likely to be an issue. In short I think you are worrying over issues that are in fact non-issues.
The &quot;Beholder&quot; was originally invented as part of AD&amp;D (2nd edition IIRC) and copyrighted by TSR (Gary Gygax and associates, essentially). WotC bought TSR and all its assets, including copyrights. There were at least two other RPGs that tried to use Beholders and other original creatures from the Monster Manual of D&amp;D and dropped them after a cease and desist order from the copyright holders. I believe one was from TSR, and one from WotC after they purchased TSR. To the best of my knowledge there was no actual copyright suit, so the validity of the copyright was never tested in court, but it is probably valid. Merely calling a creature a &quot;Beholder&quot; is not enough to violate the copyright, there would need to be actual copying of the description, or a sufficiently detailed similarity to make the use an infringement. That is always a matter of judgement, ultimately for a court in a copyright suit (or an appeals court). So, while all the possibilities mentioned in the answer by @Dale M are valid, it is additional possible that the version used by HOMM3 is not sufficiently close to the one copyrighted as part of AD&amp;D for a copyright claim to prevail, or the WotC fears that it would not prevail, and so does not spend the money to try.