If someone catches a Pokemon that is on my property, is that theft? Does something that is virtually located on your property like in Pokemon GO incur any kind of property right for the property owner?
In this answer, I address title question: "If someone catches a Pokemon that is on my property, is that theft?"1 The Pokémon is an entry in a database, presented by Nintendo to users in their mobile app and can be included in a user's collections after that user completes some in-game actions. It isn't your property. It isn't even their (the users') property. Further, a Pokémon appears for all users can be captured again and again by multiple users until it disappears for all users. One user capturing a Pokémon doesn't make it unavailable for others. The Pokémon doesn't "become subject to" any property rights of the owner of the real property that it happens to be virtually overlaid on. Said another way, it doesn't "incur" any of their property rights. Capturing it in-game is not theft. 1. The question in the question body is "does [a Pokémon] incur any kind of property right for the property owner". Incur means "to become subject to". That is different than the broader verb "implicate". This question does not ask (and this answer doesn't answer) whether the Pokémon can implicate the property owner's property rights (e.g. via attractive nuisance, trespass, etc.). Some of that is addressed at a separate question.
They have copyright in their additional text, and possibly in things like their visual design choices (fonts, layout etc). They may also have introduced a few deliberate typos to detect any literal copies from their version (rather as mapmakers add a few imaginary features to their maps). None of this creates any rights to the original text. You are still free to produce your own copies of the original text. Just get it from some other source so you can be sure not to include anything of theirs.
Assuming USA law: https://www.law.cornell.edu/uscode/text/18/2315 If you accept or buy goods that are knowingly stolen you may be fined or imprisoned. If you buy goods and later find out they were stolen you can sue for a refund. However, I'd say the likelihood of getting your money back is incredibly low.
This would be unauthorized access to a computer. The offence is found in Section 1 of the Computer Misuse Act 1990. Note that this is a criminal offence, approaching the police about it might be the best way of handling the situation (if you want to go that route, and also, I'm not a lawyer).
The part about "If I'm the owner of the content, surely I have the right to request its deletion" is the problem. Sure, you have the right to request, but you can't legally compel. You have an agreement with them, according to which you got something, and they got something. You can't then take back the thing that you gave them, which is permission to use. You didn't give them the IP itself, which you still hold. Here's an analogy. You may own a car, and can give a person permission to use the car (let's say "if you bring me back a pound of cheese from the store"). You cannot later change your mind (especially after you've gotten the cheese) a say that you retract that permission and therefore they actually stole your car. When permission to use is given, as long as the conditions for granting permission are satisfied, you can't un-give permission.
Actually, neither the council nor a private owner are responsible for illegal actions by unauthorised people on their property. This is obvious: if an intruder enters your property and, while there, shoots someone you cannot be held responsible. However ... Since you have made them aware that there are intruders on their property acting illegally and causing a nuisance to the neighbours and they have done nothing they are quite likely negligent, even recklessly negligent. Rather than sue them, consult a lawyer and get them to write a letter that if they do not take action by X date you are going to sue them.
There is ample reason to conclude that "non-commercial" would include a church, as well as advocating a political cause or candidate. The hard part of "personal". In the context of (Canadian) bankruptcy law, it can mean "non-business use"; in the context of "personal use property", it can be "A type of property that an individual does not use for business purposes or hold as an investment. In other words, property that an individual owns for personal enjoyment". US tax law takes "personal purposes" to refer to non-business purposes. But in the context of copyright (especially music downloading / copying), it is taken to refer to the use of or by an individual. Distributing free copies of a protected work does not get legally sanctioned due to the copying being non-commercial. The alternative term "private" is much clearer, in identifying "just you", but is probably avoided in this kind of context so as to avoid the wrong inference that you can only play Pokemon in the privacy of your own home. So the slightly less clear term "personal" is used instead of "private" especially in copyright-related contexts. "Personal" and "private" are not exactly the same, but when it's about use, I don't see any difference, and I think there is no question that use to attract to a church or political candidate is not "private", it is public. Since the license does not define "your own personal purposes" and there is not an existing crystal-clear definition of "personal purposes", the phrase could be given its "ordinary (plain) meaning". Of course, plain meaning has to give way to contractual intent, so we have to figure out what the parties intended. Except, you don't have a contract with Niantic, but still, plain meaning surely has some place in the law of licenses. At this point, in a lawsuit, both sides would hire an expert witness like a linguist or English teacher to make the case that a church or other non-commercial non-private use is / is not included in the meaning of "personal purpose". A silly argument could be made to the effect that if you personally have an interest in doing something then it is a personal purpose (if specifically commercial, it would be precluded by the term "noncommercial"). What makes this silly is that everybody does things for personal purposes (even acting in a way that benefits others, since you do so for the personal reason that you should do so), and thus "personal" would not mean anything. That is, "personal purposes" does not mean "whatever motivation or interest you personally have". You can also gain a certain understanding of what "personal purposes" means by looking at similar licenses. In the context of academic publishing, authors are typically granted license to copy "for personal, professional, or teaching purposes". Professional purposes and teaching purposes are things that the person has an interest in, so by mentioning these things separately, we must conclude that "teaching" is not a "personal purpose". And so: I would conclude that a court could find that using a product to support a political campaign, philosophy, or religion, is a "public" purpose, not a "personal" purpose. At the same time, at least as I understand it, a lure module is a thing that others besides yourself personally can see (I admit, I don't go), which implies that the purpose of the thing is not entirely private. In addition, there is a fair amount of buzz out there about how a lure could be good for business, which is (1) clearly in contradiction of the license terms and (2) clearly a golden opportunity for Niantic, perhaps in a few weeks after everybody gets hooked and then they will offer non-personal licenses. Their license terms also say that you will not "use the Services or Content, or any portion thereof, for any commercial purpose or for the benefit of any third party or in a manner not permitted by these Terms". I would say that that definitively says "No don't do it", and it also means that you can't be nice to a neighbor. So what they literally say and what they really intend are probably completely different things.
No It's your device, you can do what you like with it (subject to the law - you can't hit people with it. Unless they want to be hit: whatever turns you on, turns you on). However, if you do operate it outside their instructions then they would not be legally liable if it failed and injured you or someone else or set fire to the cat or whatever. The "prohibition" would limit their legal liability.