Hayama's personality is very complex, yet he's a pretty transparent person once you get to know him and learn to read him. His main characteristic is that he hides/suppresses a lot of his emotions, since after years of being basically shunned by his family, he learned to keep his feelings buried. It's not like anyone was there to understand him or treat him with kindness, so at some point he probably had to turn off his feelings just to cope with his situation.
It might seem like that's a pretty dark statement to make about a Kodocha character, but even though Hayama's family situation is presented in the midst of humor and it improves right away, it was his life for all of his 11 years. That is the basis for his character, so Hayama has a very cynical view of life and tends to expect the worst out of everyone. That's why he is usually able to see people's true intentions when they're not the best. He lacks most of the innocence he should probably still have at his age, and that lets him read adults very well and be an imposing presence before them (something Rei-kun doesn't enjoy at all).
Like Sana says, after years of hearing he was a "devil," Hayama eventually ended up believing that description and started trying to live up to it. But that's about the point in his life when he has the good fortune of meeting Sana (or the good fortune of having Sana bust into his life, I guess). She makes Hayama's family realize what they're doing to him and somehow manages to end a lifetime of suffering and isolation for him.
After that, the changes that take place in Hayama are slow and subtle. First of all, you could say that Sana restored his faith in people, or at least gave him someone to believe in. Early on he makes it very clear that he thinks that no one, including Sana, is capable of understanding him or caring about anything but themselves. But Sana proves him wrong, and in spite of himself he becomes close to her and to his family.
Once his family situation improves, we get to know the real Hayama, and his good qualities get a chance to come to the surface.
Like Sana, Hayama is brutally honest. He hates hypocrisy and feels uncomfortable making polite conversation with people he doesn't actually like. Hayama is a very good (and strict) judge of character, so he only becomes friends with people he knows are genuine. But once he becomes your friend, he's extremely loyal and protective.
Sometimes Hayama seems a bit cold and aloof, but in truth he's very contemplative and caring. Although he's not into sharing what's on his mind, what he does say often carries a lot of truth and significance (especially for someone his age). Fortunately, like most people in life, Hayama slowly learns to be better at expressing what's inside his mind and heart, simply because it's necessary for his survival.
In many ways, Hayama is almost like a small adult. He's generally very mature and clear-headed and knows how to put things in perspective. But he can be blinded by his emotions when they're strong, so sometimes impulsiveness and jealousy can mess up his life. But I think that his extreme loyalty and honesty overshadow those traits, so Sana couldn't ask for a better "best friend and enemy."
