Red Hood is a character who has been variously depicted in comics. Sometimes it's Jason Todd, who was once Robin and came back with a more violent approach.
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.
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.
Red Hood doesn't kill Hawk in the comics. The relationship between them is complex and involves various interactions, but killing each other isn't part of it. The comic writers chose a different path for their characters' development.