Those four chapters are involve quite a few pages, themes and events, so I'm not sure how possible a brief summary is, but I'll give it a shot.
In chapter 10 of Fools Crow, we see White Man's Dog coming into his own in the tribe, gaining status and respect as a young man, and his marriage to Red Paint takes place. This chapter and Part 1 conclude with White Man's Dog dancing at the Medicine Pole during the Sun Chief ceremonies.
Chapter 11 and 12 is where White Man's Dog and the war party are journeying to the Crow camp to go to war, and he gets his new name. It involves the raid on the Crow tribe, how White Man's Dog accidentally does well, and earns his name Fools Crow. It is also where Fast Horse screws up and Yellow Kidney is captured and tortured because of it.
Chapter 13 sees White Man's Dog being renamed formally, and recognized for his acts during the war party's attack. It is also the first appearance of "Napikwans", whites as they make contact with the tribe. They are soldiers - "Seizers" and this causes great concern.
Chapter 14 has Fools Crow in a one-on-one showdown with a mountain man, one that is very good at combat and the ways of the hills, so that Fools Crow is himself almost killed, but triumphs in the end. They also talk of Owl Child and his crimes against the whites, and what that means for the tribe.