The dream that both Hassan and Amire share is the one that they save the people by defeating the sea monster in the lake.
Amir is selfish and Hassan is humble and loyal to Amir. Hassan is a Hazara, Amir is a pashtun. Amir is granted to right to get an education, Hassan is not.
Because, even after everything that happened, he still feels loyalty towards Amir. It is the final sacrifice he makes for him. Also Hassan knew that if Baba found out Amir lied, he was be in serious trouble.
Hassan uses a slingshot to defend himself and Amir against Assef when he tries to attack them. Hassan ultimately sacrifices himself by getting severely beaten rather than giving in to Assef's threats.
Hassan chooses not to tell on Amir because of their strong bond of friendship and loyalty. He values their relationship above all else and is willing to protect Amir, even at the cost of his own reputation or safety. Additionally, Hassan may feel grateful for the kindness and care Amir has shown him in the past, leading him to forgive any wrongdoings.
Actually, they are half brothers. Amir had found out that when Rahim Khan had hinted that Ali was not Hassan's father but Baba was (which explains why Baba had a closer relationship to Hassan and Amir).
Amir frames Hassan for stealing money and a watch, knowing that Hassan will take the blame to protect him. Amir stands by and does nothing to stop it, thus indirectly getting both Ali and Hassan in trouble.
Amir threw pomegranates at Hassan out of frustration and jealousy stemming from their complex relationship and his own insecurities about his father's affection for Hassan. This act was an expression of Amir's conflicting emotions and desire to hurt Hassan in the heat of the moment.
In Khaled Hosseini's "The Kite Runner," Rahim Khan reveals to Amir that Hassan, Amir's childhood friend and servant, was actually his half-brother. This shocking news comes after Amir learns that Hassan was murdered by the Taliban, and Rahim Khan urges Amir to return to Afghanistan to redeem himself by rescuing Hassan's son, Sohrab. This revelation forces Amir to confront his past and the choices he made, deepening the themes of guilt and redemption in the story.
Ali tells Amir that Hassan mostly runs errands and does chores for him now, as he is getting older and can no longer do physical work like he used to.
1.Memory: The first memory indicates of their bond of "brotherhood" because they drank from the same breast signifying how "strong" their bond is. 2. Memory: In the second memory, the old man "sees" something ominous in Hassan's future ( the rape possibly) so he gives back the rupria. Amir pulls back his hand because he doesn't want to hear possible bad things occurring in his life. 3. Dream: Amir is alone in the snow with no one to help, just like Hassan in the alley, but in Amir's dream he gets help by and unknown person (possibly Hassan) with injured hands (allusion to Jesus and the stigmata), but in Hassan's case Amir doesn't know if he would help Hassan or leave. Regarding the allusion to Jesus: Hassan is sacrificing himself for someone else, just like Jesus. If the hand was Hassan's it only strengthens the allusion of Jesus with his nailed palms (stigmata).
Amir and Hassan, the sultans of Kabul
Hassan and Ali give Amir a leather-bound notebook for his birthday.