Here are some quotations from Chapter 6 about Holden's fight with Stradlater:
After asking if Stradlater gave Jane "the time" in Ed Banksy's car, this is what Holden says:
"The next part I don't remember so hot. All I know is I got up from bed, like I was going down to the can or something, and then I tried to sock him, with all my might, right smack in the toothbrush, so it would split his goddam throwat open."
Holden's character is revealed even more when Stradlater has straddled Holden and is holding him down. Holden keeps talking about Jane's chess techniques:
"I told him he thought he could give the time to anybody he felt like. I told him he didn't even care if a girl kept her kings in the back row or not, and the reason he didn't care was because he was a goddam stupid moron."
The second part of this question is wide-ranging and there are examples from nearly every chapter that illustrate Holden's social skills problem. In fact, his decision to fight Stradlater suggests some type of self-punishment.
The red hunting hat is one of the most used symbols in this novel that demonstrate Holden's social problems. He puts the hat on whenever something bad happens. He treats it like a shield, or like something that makes him invisible. After his fight with Stradlater, Holden put the hat on "and turned the old peak around to the back, the way I liked it, and then I went over and took a look at my stupid face in the mirror." He puts this hat on several times throughout the story.
Lying is another example of Holden's social skills problems. When he leaves Pencey and takes a train, he has a conversation with Ernest Morrow's mother and lies the entire time.
Holden also fails to pick up on social cues. In his cab ride to New York, the cabbie is pretty obviously annoyed with Holden, but the boy still asks him to stop and get a drink with him.