In the second scene (the restaurant scene) of Death of a Salesman, where does the conflict lie and how is the conflict developed or resolved?

In the restaurant scene, Biff and Happy are supposed to be meeting Willy and Biff is supposed to report on his visit to Bill Oliver to ask for a loan. Happy gets to the restaurant first, and Biff arrives before Willy does. Before Willy gets there, Biff reveals to Hap that Oliver only saw him for a minute and that Biff ended up stealing Oliver's fountain pen. Fleeing from the office, Biff has a revelation. He finally realizes that he has been engaging, along with Hap and Willy, in rewriting his history. Although they have all pretended Biff was a salesman with Oliver, in fact he was only ever a shipping clerk, and he stole some balls from Oliver when he worked for him previously. Having finally faced the truth himself, Biff wants to get Happy, and more importantly, Willy, to face reality.

Happy strenuously objects to Biff's idea, telling him he is crazy. Biff insists, "Hap, he's got to understand that I'm not the man somebody lends that kind of money to. He thinks I've been spiting him all these years and it's eating him up." In other words, Willy believes that Biff deliberately sabotages himself in order to punish his father.

This relates to the conflict between Biff and Willy that goes all the way back to Biff's senior year in high school. Biff had failed his math class because he was too focused on sports. That meant he couldn't get into the University of Virginia because he didn't have enough credits. Biff surprises his dad at his hotel room in Boston because he wants Willy to come back home and talk to the math teacher before school closes for the year. Biff learns that Willy is having an affair and he actually sees the "woman." Biff's response is to burn his University of Virginia tennis shoes, and after that he never succeeds at anything he does. Willy interprets Biff's behavior as "spite" towards him. After the revelation Biff received after seeing Oliver, he now accepts that his failures are his own, not Willy's, and he wants to share that with Willy so that Willy will stop being tormented by Biff's failures.

Back at the restaurant, Biff tries repeatedly to share the reality of what happened at Oliver's. Hap keeps interrupting with deceptive comments, trying to lie to Willy to make him think Biff had been successful. Happy believes it is best to keep lying to Willy because "Dad is never so happy as when he's looking forward to something." Happy sees no value in telling the truth; he thinks of short-term consequences only while Biff wants to bring about an actual resolution to the problem. Willy also keeps interrupting Biff's story, first to try to interpret it in a way that makes Biff look good, and then blaming Biff for ruining the opportunity. Biff lies about having an appointment with Oliver the following day, then says he can't go because of the pen. Willy accuses Biff of spiting him and strikes him. As Willy becomes more upset, he loses touch with reality and goes into a flashback in his mind of the time Biff came to Boston. Willy wanders into the washroom and the boys leave him behind.

The restaurant scene ends with Biff having been able to tell his father some but not all of the truth, but Willy still believing Biff fails on purpose to punish his father. After Willy goes to the washroom, Biff shows the hose to Hap and lets him know Willy plans to commit suicide. He pleads for Hap's help, but Hap goes off with the women he has picked up.