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 appears to claim a monopoly on the right to publish literary reference guides, and other non-academic research, relating to her own fiction. This is a right no court has ever recognized. It has little to recommend it. If accepted, it would dramatically extend the reach of copyright protection, and eliminate an entire genre of literary supplements: third party reference guides to fiction, which for centuries have helped readers better access, understand and enjoy literary works.
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.