Why does Josh vacillate between his given name and "Filthy McNasty"?
Nicknames are an important component of the text. Sometimes, they're given to a character; sometimes, they're insisted upon by that character; sometimes, they wear out their welcome. Josh's nickname is from Dad, and it encapsulates his skill on the basketball court. It connotes his charm, his talent, his controlled aggression, and his showmanship. However, it represents only one facet of his personality, and as he starts to watch JB change and Dad face health issues, he starts to eschew "Filthy" and return to "Josh." Josh is a more multi-faceted name that includes his status as a son, brother, student, friend, potential boyfriend (he wishes!), and, still, basketball star. Josh doesn't want Dad to call him "Filthy" anymore, especially as Dad grows sicker and sicker, because he wants Dad to see him as more than just a basketball player.
What leads JB to finally forgive Josh?
JB is justifiably shaken when Josh demonstrates aggression towards him, and he refuses to talk to him or accept his apology for a long time. However, Josh does not give up, and that contributes to JB's realization that his brother is truly sorry. Josh's letter is a big help because it is honest and moving; his small gestures like letting JB study off of his notes help further; and, finally, Dad's death cements the fact that they are family and family is important above all else. As Josh learns from his mistakes, JB learns to forgive Josh and move on. The two of them are "Da Man" now: they are living embodiments of their father, and they work best when they are in harmony with each other.
Why doesn't Chuck want to acknowledge that he is sick?
Chuck is a very good and very loving father, but he has a massive blind spot that he does not heed until it is too late. He suffered his own trauma watching his father die in the hospital, and he concluded that doctors and medical institutions were problems. This conviction seemed to only grow over time, to the point that Chuck decided to forego a chance to try out for the Lakers because he was too afraid to have surgery. Self-delusion also comes into play, because Chuck clearly experiences symptoms of hypertension and heart trouble but has convinced himself that he's fine—he simply ate something bad, played too hard, etc. The narratives he tells himself are incorrigible, and Mom's insistence that he make a doctor's appointment can barely make a dent in them.
What do references to jazz and hip-hop contribute to the novel as a whole?
Dad loves jazz, a musical form that is a corollary of basketball in its improvisational nature, its energy, and its reliance on the team/other musicians with the opportunity for a single figure to occasionally shine. Jazz's meaning is embedded in what seems like chaos, just like the meaning found in life. Hip-hop is found not only in the stated rappers that the twins are listening to but also in the rhythms of some of the poems. These poems have vibrant, sometimes aggressive words and structures; they are full of life, anger, beauty, and zest for life.
What do vocabulary words contribute to the novel as a whole?
The vocabulary words reference Josh's education and his youth; studying and learning are major components of this 12-year-old's life, and he (mostly) takes that seriously. But, more importantly, these words help him to define himself and understand the world at large. He learns the meaning of "calamity" while he is experiencing calamities, and understands when his own "tipping point" was. He realizes Mom is right in deeming him "churlish," which pushes him onto the path of self-reflection and atonement. He begins to grapple with his loss through the word "starless," as his Dad is out of his life and his life is starless. These words are thus conduits to understanding and growth.