Translation:Was that book interesting?
I agree. These two words are chosen based on the act/object involved.
Only omoshiroi: books, comics, movies, comedies. Only tanoshii: dates, parties, sports, talking with someone. Both: describing people (he's an interesting/funny guy), speeches.
I think the nuances are mostly the same as English interesting (omishiroi) and fun (tanoshii).
面白い - interesting or funny (amusing - giggle-worthy).
楽しい - fun as in enjoyable.
おかしい - funny as in hilarious, tears streaming down your face level laughing. Also crazy/strange as in 'funny in the head'.
Not to be confused with おかし - lollies, sweets, candy, treats etc
No, what is used here is the past tense of an i adjective. The rule is to remove the final い and then add かった. In Japanese, when you want to say something was something else by qualifying it with an adjective, you can do this by directly conjugating the adjective in this manner. Note that there are two classes of adjectives with their own conjugation rules.
Not necessarily. In conversation about the book, the polite way to refer to something is その. So if you were speaking a long time about (perhaps gossiping) another person, who lives in another town, you could start referring to that person as その人 instead of あの人. Evrn though あの人 would technically be correct, その人 is more polite.
The same holds true for other subjects, such as その本. It's just more polite and one of those things you learn
Adding でした would make it more formal. Its one step away from the most formal 面白かったでございます.
So in terms of formality 面白かった! Least formal (you would use this with your friends) 面白かったです. 面白かったでした. Middle ground(use this with your boss) 面白かったでござる. 面白かったでございます. Most formal. (You would use this when speaking with the master of the household where you work as a servant, or if you were Kenshin...)