A good example you can study is the Harry Potter Lexicon case. A fan site wanted to publish a guide to the Harry Potter universe. Rowling disagreed, claiming she owed all the rights to the Harry Potter world, and nothing could be published about it without her approval. The case went to court, & Rowling mostly lost (except on minor points). The judge said:
In support of her position Ms Rowling appearsJudge Patterson said that reference materials were generally useful to claim a monopoly on the right to publish literary reference guidespublic but that in this case, and other non-academicVander Ark went too far. He said researchthat "while the Lexicon, relating to her own fiction. Thisin its current state, is not a right no court hasfair use of ever recognized. It has little to recommend it. If acceptedthe Harry Potter works, it would dramatically extendreference works that share the reach of copyright protection, and eliminateLexicon's an entire genrepurpose of literary supplements: third party reference guides to fiction, which for centuries have helpedaiding readers better access,of literature generally should be encouraged understand and enjoy literary worksrather than stifled.
Answering your other questions, it would be better to go with a publisher, as the copyright owner may sue anyway, and the publishers can afford better lawyers than you. I'm sure if the book had been self published, the author would have been bullied into backing off due to the high legal costs.
I don't think the rules would change based on the medium, but not sure. I don't think so, because I have seen such unofficial guides to TV shows, books, video games, to mention a few.