What if after a patent is awarded, someone proves they invented it earlier? I'm referring to a US patent. (USPTO non provisional Utility patent) And I'm referring to that first inventor not only proving they thought of it, of course, but that they published the idea or even offered a product with it for sale (obviously not successfully, else the USPTO would have noticed it). Would that invalidate the patent? Would the patent hold except to with regard to this first inventor? Something else?
Under the America Invents Act of 2012 nothing would happen unless someone - the original inventor or any third party - filed for an Inter Partes Review. The cost of filing to try to get an IPR going is $15,500. If the published information about the original inventor's work passed some hurdle, an IPR can be instituted by the USPTO. It is a trial-light proceeding that is estimated to cost at least $100,000. Any claims that are found invalid are invalid for everyone (pending any appeals). The AIA did introduce a new "feature" that could help you hypothetical first inventor to stay in business if he/she was actually producing and selling the thing. It is called "prior user rights" and lets you keep making what ever you were making at the location you are making them at. It is not automatic. Rather it is a defense in an infringement suit. Even before the AIA there was no such thing as "have the patent canceled". The issue of the first inventor's prior art would come up at a patent infringement lawsuit.
Amazon and most similar vendors (e.g. Wal-Mart) requires vendors to warrant to them that the products sold do not violate intellectual property laws and indemnifying Amazon for any harm it suffers if the representation is inaccurate. (I came to learn this in intellectual property litigation involving a Wal-Mart supplier and in separate patent infringement attorney malpractice litigation involving other vendors of different firms.) But it doesn't generally do any independent due diligence to confirm that these representations are true. As a practical matter, determining if something infringes any existing patent is a non-trivial matter, and even in cases where patent infringement lawsuits are brought by lawyers in court who have done due diligence, the validity of the patent is upheld in only about 50% of the cases that go to trial. The basic problem is that there is no definitive way to index patents that isn't vulnerable to an invention which is infringed being described in a different way than you are conceptualizing it for your search. Generally speaking, simply buying a patent infringing good as an end user in the good faith belief that it is not infringing is not a violation of patent law or actionable, and the knowledge that large firms require representations with legal consequences from their vendors probably suffices to show good faith. But if you plan to use the purchased good in some product that will be resold to others that incorporates it, that might be an infringement. If you are a prospective vendor, there are firms that specifically do patent searchers to determine if there is an infringement, but they aren't cheap. Typically the fee would start at $5,000-$10,000 and go up from there, and typically that is for a non-guaranteed search. An opinion letter from a patent practitioner would be necessary to be really sure (assuming that the patent practitioner or non-patent practitioner search doesn't find a clear infringement which could happen quickly and be cheap by comparison) and that would be much more expensive, maybe $25,000-$100,000, if it wasn't a particularly close case. On the other hand, if what you are primarily concerned about is the design of the bit that plugs into the Apple product, rather than all aspects of the product, it is a relatively trivial matter to determine if the connector involves an industry standard which is either in the public domain or widely available for license at a modest price for manufacturers, in which Apple does not itself claim a patent, or a proprietary design, in which Apple claims rights. USB-C connections, for example, are an industry standard connector, discussed here, which would give you some further leads. In contrast, earlier Apple-promoted (and developed) Lightning and MagSafe connectors, are proprietary connectors, which would potentially be infringing and would require more analysis.
All your work is yours. They've made it very clear it wasn't a work for hire, so it's yours. They can't copyright any of their ideas. You can't copyright an idea. Only specific creative elements authored by them and present in your work could be covered by copyright. You didn't use their block diagrams. I don't see how references to other sites to look at would constitute a creative element they authored. That said, you probably want to talk to a lawyer and get a written legal opinion that you can rely on.
This is called a qui tam action. It's a concept that's been around a long time in the English legal system (predating the US), to encourage people to help the government enforce its laws. The more contemporary system is to give private parties the right to sue on their own behalf for some wrong (known as a "private attorney general" system), which is how things like civil rights claims tend to work; the difference with qui tam is that the government is the plaintiff (source) It's possible when the law says that a claim under some section may be filed by a private person on behalf of the government; at the time the article was written, the false marking statute (35 USC 292) stated that "Any person may sue for the penalty, in which event one-half shall go to the person suing and the other to the use of the United States." In a qui tam action, the government is the plaintiff; it's just that instead of a public attorney handling the case, it's handled by a private party. There were three active qui tam statutes in US federal law as of 2009 (source: CRS): the False Claims Act (31 USC 3730), the patent marking claim, and an Indian protection statute (25 USC 201). The patent marking qui tam provision has been repealed, leaving just the two. For the Indian protection statute, I can't find any reference to any special procedure; for the False Claims Act, there is a special procedure included in the law. In the False Claims Act, when an action is submitted, the government is notified and the complaint kept sealed for 60 days while the US government decides what to do. If the government wants to take over the case itself, it can do that; if it wants the private party to run the case, it can do that too; if it wants to dismiss or settle the case it can do that as well. It can also ask for the time to be extended, or for discovery to be delayed to gather evidence or prosecute a separate criminal or civil case. If the government lets the private party run the case, they can still intervene later if they have a good reason. After the case finishes, the private party gets 15-25% of the judgment or settlement (if the government took over the case) or 25-30% (if the private party ran the case), plus attorney fees. If the facts the case was brought under were publicly known when it was filed, the amount shrinks to 0-10% if the person supplied information to the government that wasn't publicly known when it was supplied, and the case is dismissed if the person just learned about it from public sources. For the false marking statute, a district court actually found it unconstitutional in part because of the lack of the extensive procedure found in the False Claims Act. There, the procedure was just to file the case like normal; the clerk had to tell the Patent Office that a claim had been filed within a month, but one issue was that a settlement could have happened in that time and bound the government. It's possible higher courts would have ruled had that section not been repealed later that year. As for other countries, the idea came to the US from England, but the Common Informers Act 1951 eliminated it there. However, private prosecutions (which do exist in England) are similar in that the case is on behalf of the Crown, but handled by a private party; they're different in that the private party doesn't get any part of the judgment. While it's hard to prove a negative, I can't find any evidence of qui tam provisions outside the US.
20th Century Fox have a trademark on "Simpsons." They have trademarks on "Bart Simpson", on "D'oh", on "Duff Beer". I would assume that they take their trademarks seriously. What you can't do is to use someone else's trademark to make people believe your commercial product is related to theirs. It's quite reasonable to assume that someone seeing your book in a store would think it is written by the makers of The Simpsons show and therefore buy it. Even if you say that isn't your intention, it is what would happen. I'd try coming up with some different titles, maybe "How to write animated TV shows" with "Example: The Simpsons" (well, you are the writer so you should come up with something better), and take them to a lawyer. And then contact the makers of the show (again asking the lawyer for advice how to do this) because even if your lawyer says the title is fine, that doesn't mean you can't be sued.
You cannot use a patented invention without permission A patent gives the owner exclusive rights to use it: not just profit from it. The only way you can use their patent is by licensing it. You cannot make any version of the software that uses the patented method, free or otherwise. Technically, the software you have now is infringing even if you never release it. If you had published your work before they filed for the patent, you can seek to have their patent invalidated due to the existence of prior art. If you had been using it privately prior to this some jurisdictions will allow you to keep using it privately.
You can't patent an algorithm, but I'll assume you are talking about the case where you have patented a machine or process that uses an algorithm, but that adds significantly more, and that the software being distributed implements much of this process. Courts might find an implied licence or promissory estoppel when distributing software under an open source licence that doesn't explicitly exclude patent licencing as part of its terms. It would be prudent to state your patent rights and explicitly exclude a patent licence if you intend to enforce your patent rights. As an example, this software implicates a patent , so they allow "permission to use, copy, modify, and distribute this software and its documentation for educational, research, and non-commercial" purposes. Users that want to use the software commercially need to contact the authors who also happen to be the patent owners, and I assume would negotiate a patent licence at that point.
It is cl;early not legal to charge for an optional warranty without ever having gotten approval for it. The customer could simply ask for a refund on teh ground that this was an error, and take it to small claims if that was refused. I am sure it is legal to offer such an optional warranty and point out its (alleged) benefits. I do not know if consumer law forbids making this pitch multiple times in the same selling encounter.