(1) To the best of my knowledge, you are 100% correct.
(2) I think that most books would classify "about the war"
as a prepositional phrase that modifies (belongs to) the word
(a) "about" = preposition
(b) "the war" = object of the preposition.
Tom: Do you want to see a new Russian film with me tonight?
Mona: Sure! What's it about?
Tom: It's about the war.
Mona: Oh, I'm sorry. I don't like movies about the war.
Tom: OK. Would you be interested in a film about the Bolshoi Ballet?
Mona: That would be great!
***** Have a nice day!