Here, Amir and Hassan are using a shard of a mirror simply to be annoying boys. But the definition hints at the more significant meaning of the image. The novel is written as a first-person memoir, which is essentially looking into a mirror, reflecting on oneself, and shining light onto specific memories to make sense of one's life. The shard represents the nature of memories, especially those that are difficult to remember or face.
When we were children, Hassan and I used to climb the poplar trees in the driveway of my father’s house and annoy our neighbors by reflecting sunlight into their homes with a shard of mirror.
Here, Amir and Hassan are pelting each other in a teasing way, but this scene contrasts with two later scenes where the more violent and militaristic meaning of "pelt" (as seen in the definition) is shown.
We took turns with the mirror as we ate mulberries, pelted each other with them, giggling, laughing.
The curved wall led into the dining room, at the center of which was a mahogany table that could easily sit thirty guests— and, given my father’s taste for extravagant parties, it did just that almost every week.
People had raised their eyebrows when Ali, a man who had memorized the Koran, married Sanaubar, a woman nineteen years younger, a beautiful but notoriously unscrupulous woman who lived up to her dishonorable reputation.
add a flaw or blemish to; make imperfect or defective
They said Ali had married his cousin to help restore some honor to his uncle’s blemished name, even though Ali, who had been orphaned at the age of five, had no worldly possessions or inheritance to speak of.
(anthropology) relatedness or connection by blood or marriage or adoption
Another definition of "kinship" is "a close connection marked by community of interests"--this also fits the example sentence, since Amir and Hassan shared the same wet nurse and grew up with each other, but as far as they knew, they did not have any blood, marriage or adoption connections. But in using the word "brotherhood" Ali is emphasizing the first definition.
Then he would remind us that there was a brotherhood between people who had fed from the same breast, a kinship that not even time could break.
My father was a force of nature, a towering Pashtun specimen with a thick beard, a wayward crop of curly brown hair as unruly as the man himself, hands that looked capable of uprooting a willow tree, and a black glare that would “drop the devil to his knees begging for mercy,” as Rahim Khan used to say.
When people scoffed that Baba would never marry well—after all, he was not of royal blood—he wedded my mother, Sofia Akrami, a highly educated woman universally regarded as one of Kabul’s most respected, beautiful, and virtuous ladies.
Sometimes, my entire childhood seems like one long lazy summer day with Hassan, chasing each other between tangles of trees in my father’s yard, playing hide-and-seek, cops and robbers, cowboys and Indians, insect torture—with our crowning achievement undeniably the time we plucked the stinger off a bee and tied a string around the poor thing to yank it back every time it took flight.
Two other definitions of "nemesis" are "an unbeatable rival" and "one that inflicts retribution or vengeance": while the tenth-century Persian warrior Sohrab might've been Rostam's unbeatable rival at one point, when Rostam finally beats him, that causes him misery. All three definitions could apply to the twentieth-century Afghani bully Assef, who is Amir and Hassan's nemesis.
Rostam mortally wounds his valiant nemesis, Sohrab, in battle, only to discover that Sohrab is his long-lost son.
Although the twelve-year-old Amir felt that winning the kite tournament was a matter of life and death (or at least not being a ghost to his father), the older Amir as the narrator invests the word "viable" with more significant meaning, because he knows that his choices after winning the tournament led to unviable situations for Hassan.
I was going to win. There was no other viable option.