What are Amir's feelings after finding out that Hassan is his half brother? Did he ever have any idea that this could have been possible beforehand?

Amir experiences several feelings all at once.

First, he is angry with his father. He is angry because he always felt as if his father favored Hassan over him, and sometimes even felt his father loved Hassan more--now he understood that yes, in fact, his father did have those feelings, which arose out of his own guilt and shame.

He is also mad at his father because his father said the worst thing you can do in life is steal, and his father used the example that even lying is a form of stealing--when you lie you steal the truth from someone; he is angry because his father, the entire time, was lying to him, stealing the truth about Hassan's parentage.

Second, he feels increased guilty. It was one thing to have let his friend be raped in an alley, but to now know that Hassan is his brother makes the reality of what he did even more painful.

Third, he feels sorrow. He feels like if he had known this fact that things would have turned out very differently for himself and Hassan and their relationship.

As far as Amir knowing this beforehand, this information is definitely alluded to, especially in the beginning of the book--Baba always invites Hassan to go everywhere and always gets him birthday presents and treats Hassan very well. This leads to Amir's feelings of jealousy, which leads to Amir allowing the rape to happen in order to gain favoritism and higher standing in the eyes of his father.