One popular one is 'The Dark Knight Returns'. It's a classic that redefines Batman in a darker, more gritty way. The art style is distinct and it has a great storyline that explores an older Batman coming out of retirement.
I don't think so. To the best of my knowledge, Red has no significant presence or role in DC Comics. DC has a vast array of characters, but Red isn't among them.
Sure. 'Superman: Red Son' is a great start. It presents a different take on Superman where he lands in the Soviet Union instead of the United States. It's easy to follow and has amazing art.
The red in DC Comics often represents passion, power, or danger depending on the context and character. It's a visually striking color used to convey various emotions and traits.