In what sense are Melba and the other eight students "warriors"? What qualities do warriors have? How do these qualities help the Little Rock Nine throughout the school year?

Warriors are traditionally thought of as being strong, often in the context of war. The kind of strength shown by Melba and the other students may not be the martial strength normally associated with warriors, but one can recognize it as such all the same. And although the war in which they're engaged doesn't involve the use of physical violence (at least not on their part) they are actively involved in a struggle—one that draws upon every ounce of physical courage, no less than the bloodiest of battles.
The Little Rock Nine must run the gauntlet of hate-filled mobs each time they go to school, and that takes enormous courage. These students are warriors in that they're fighting for something: the right to an equal education. This fight is difficult enough as it is, but it would have been so much harder if the students hadn't stuck together, didn't show group solidarity in the face of extreme adversity. But that's precisely what they do, and it's what they need to do in order to overcome the numerous obstacles placed in their path.