My default, which I see no reason to depart from here, is that a word in a rulebook should be interpreted as having its ordinary dictionary definition, unless the rules otherwise define the word or provide context for an understanding different than that definition (e.g., when written such that the ordinary definition of the word is nonsensical).
Therefore, for your Question 1 (what constitutes an acronym), like aghagh did, I would turn to the dictionary. Here are some definitions for the word acronym from major English-language dictionaries:
Dictionary.com: a word formed from the initial letters or groups of letters of words in a set phrase or series of words and pronounced as a separate word.
Merriam-Websters: a word (such as NATO, radar, or laser) formed from the initial letter or letters of each of the successive parts or major parts of a compound term.
(NB: It's also worth noting that the notes of Merriam-Websters specifically say that initialisms are acronyms, invalidating the disctinction you said some players had made, which pjt33 noted)
Oxford English Dictionary: A group of initial letters used as an abbreviation for a name or expression, each letter or part being pronounced separately; an initialism.
Thus, I would say LOL and OMG are both acronyms that count because each is a word formed from the initial letter or letters of each of the successive parts. Further, as at least two major English-language dictionaries point out, initialisms are acronyms. And if the dictionaries aren't enough for you on this point, even
the rules themselves use an initialism (FBI) as an example of what constitutes an appropriate acronym.
As for Question 2 (whether acronyms where a letter or series of letters represent the Mystery Word itself are permissible), I think it would depend on your preferred method of rules interpretation and thus think both allowing them and not allowing them are reasonable conclusions until the game's rules make it clear one way or the other. That being said, I would argue they are valid.
First, none of the items on the list of what makes a clue invalid in the rules is something like "it is an acronym that contains a constituent part that is the Mystery Word" and therefore LOTR would be valid for a Mystery Word of "Ring."
Second, since special characters like $, £, #, and " are valid, presumably including for the words dollar, peso, pound, number, and quote, and each of those symbol's names are dollar/peso sign, pound sign, number sign/hashtag, and quote/quotation mark, then I think there is already an example of permitting something as a clue even when the Mystery Word is somehow a part of the clue itself. Moreover, it's not compeltely clear what the boundaries of "special characters" is, but again, assuming a dictionary definition of something approximating one of the following, then ✈ (an airplane symbol) would be permissible for airplane:
Merriam-Websters: a symbol used in writing, typing, etc., that represents something other than a letter or number.
Your Dictionary: a symbol that is not an alphanumeric character.
Third, I think the main point or purpose of the invalid clues list is to prevent giving away the Mystery Word too easily and to make people think of creative clues (as opposed to the easiest ones possible) and thus work in conjunction with the cancelled words rule for the same general purposes. Therefore, I think acronyms that contain a letter or series of letters that represent the Mystery Word are generally fine because they will not necessarily give away the Mystery Word too easily, even in conjunction with other clues, and often take more creativity than the first thing that comes to mind. For instance, with LOTR, the clue could be Ring. But it could just as easily be Lord, Elf, Troll, Orc, Dwarf, Fellowship, King, etc. For many people, something like "wedding" or "engagement" also probably came to their mind well before LOTR (unless they just finished engaging LOTR media). The same is not true when you give a word that is a homophone of the Mystery Word, the Mystery Word in another language, or a word in the same word family. For instance, "flour" with "rose" and "daisy" as a clue make it extremely obvious that flower is the Mystery Word. It also requires no real creativity. Similarly, "verde" with "color" and "chlorophyll" as clues make it extremely obvious to anyone who knows even a few basic Spanish words that the Mystery Word is green. It also requires no real creativity, just translation. Likewise, clues of "workout" and "working" and "worked" -- all of which would be in the same word family -- would make it too obvious that the Mystery Word is work, and they would require no real creativity.
Fourth, I think this rule becomes more apparent when you consider that acronyms that would overlap with another word (including another acronym) without either word overlapping the Mystery Word would cancel each other out under the same logic. If such overlapping acronyms did cancel eachother out, then "Laser" and "Emissions" would cancel as would "NASDAQ" and "Association," "BMX" and "Motor," and "SO" (for "significant other") and "ESOL" ("English for Speakers of Other Languages"). However, those word pairs are very different from each other, so much so that cancelling them would not only feel very weird but would, to me, feel like I was mechanically applying the rule without adequately thinking about why the rule existed. Some acronyms also stand for multiple things, which would make cancelling them out on that basis extra tricky. For instance, LOL can mean "laugh out loud" or "lots of love," the F in SNAFU can be a few different things depending on the levels of profanity permitted, and the aforementioned "SO" can be "significant other" or "sheriff's office." If the Mystery Word is Happiness, then the acronym "LOL" could easily go either way -- if the other clues include "Love" and "Laughter," then which are you cancelling? Both? Does the word become a Schrödinger's cat of sorts?
