The book does not clearly say what the source of Curley's anger was. However, it does intimate a few things. 

First, the book says that Curley was small in stature. It also says that because of this he hated big guys. Here is the text:

The swamper considered . . . . “Well . . . . tell you what. Curley’s like alot of little guys. He hates big guys. He’s alla time picking scraps with big guys. Kind of like he’s mad at ‘em because he ain’t a big guy. You seen little guys like that, ain’t you? Always scrappy?”

The point is that Curley was insecure. So, he had to overcompensate when he felt threatened. 

Second, Curley also felt entitled, because he was the boss's son. There are a few places in the book where this detail in mentioned. In light of this, we can assume that Curley felt that he could get away with certain things, because he had power on the ranch. So, he could get angry and get away with it. Who would stop him? 

Third, Curley was also a fairly successful boxer. So, he was able to back up his anger with physical force at times. 

Lastly, another details that emerges several times is that he felt insecure in his marriage. He was always looking for her and suspicious of other men. So, when things were not going well with his wife, it would turn into anger. 

If we add all these details together, we see that he was insecure and entitled and this combination led to anger. 

Curley is a very angry young man. If you check out the Enotes summary, you will find an excellent summation of Curley.

Now, on to your two questions: One, Curley is described as a former boxer, but at heart he is really a coward. That fear turns into self-loathing, which in turn he channels into his macho posturing and bullying. He takes out his frustrations on Lenny, as the man is taller than him (implied) and he can also act without fear of reprisal. This of course doesn't keep, as Lenny finally crushes Curley's hand.

Two, the result of his anger. Curley's wife, it is implied, flirts with the workers. She is alone with Lenny and as a result, dies. Curley uses this to whip the workers into a frenzy, setting up the final tragic event in the novel.