How would you characterize Sam and Hallie's friendship?
I personally would not characterize Sam and Hally's relationship as friendship. That doesn't mean I think they are enemies or something like that. I just think it is improper to call them friends. The age gap is too large, for one reason. But my main reason for hesitating to call it friendship is that I think a better description of their relationship is to call it a father and son relationship.
Hally's father is a deadbeat and a drunk. He might be wealthy enough to have servants, but he's still a terrible father. During the play, the audience learns that Hally's father is in the hospital and Hallie tries to convince his mom to just leave him there. She refuses, and Hally becomes violently angry upon learning that his dad will soon return home. That's not the image of a kid that loves his father. Sam's reminiscing about he and Hally making and flying a kite and doing homework together IS the image of a loving father and son. In fact, for a major chunk of the play, the two enjoy some verbal sparring with each other. They discuss how well Hally is likely to do on his upcoming exams and who are some of the greatest thinkers in history. They tease each other even.
Unfortunately, by the end of the play, their relationship is completely broken and in ruins. Hally vents his anger toward Sam, spits in his face, and insists on Sam calling him Master Harold. The last part cements the broken relationship. It is no longer surrogate father and son; it is now master and servant.