How do elements from Amir's past shape his present and future?

It depends what you fix as "present" - when he settles in America?

The main driving force in Amir is his sense of shame at the way he had treated Hassan during their childhood.  He can't make it up to Hassan, but he respects Soraya for her honesty and courage (two traits he himself is lacking at the point when they marry), and later goes to great ends to find Sohrab(Hassan's son) and to rescue him from the clutches of Assef.

Amir seeks and ultimately finds peace with himself by becoming a better person. He becomes loyal and honest, and even courageous (when he fights off Assef). The scar Amir gets is a sign that he has been acquitted of his former wrongdoing, and the final kite-running scene is a very moving one of reconciliation - with others, but especially with himself.