For example, could I make an app and release it, but it uses the titles of anime and its characters? Would it be illicit to make revenue off of it?
That depends. Simple references to the characters or anime being a real-life thing are typically allowed but any anime artwork or audio would have to be transformative or for educational purposes to fall under fair use.
As an example your app can ask 'Goku is the protagonist of which anime?' and list Dragon Ball as an answer, but you can't put a straight clip of Dragon Ball on your app without permission.