Yes, it is widely considered highly accurate.

The film is based on the Pulitzer Prize-winning biography American Prometheus. While some timelines were condensed and dialogue dramatized for cinematic effect, the major events, political machinations, and character portrayals closely adhere to historical records.

Director Christopher Nolan used color to represent Oppenheimer's subjective perspective (his personal experiences, visions, and emotions) and black-and-white to represent Lewis Strauss's objective perspective (the external, political view of events and the confirmation hearings).

No, but they didn't use CGI either.

Nolan recreated the Trinity Test using practical effects, including a combination of gasoline, propane, aluminum powder, and magnesium flares to simulate the mushroom cloud and the intense brightness of a nuclear explosion without using actual nuclear material or computer-generated imagery.

The final conversation reveals that Oppenheimer wasn't confessing to Einstein about starting a chain reaction that would destroy the atmosphere physically, but rather metaphorically.

He realized that by creating the bomb, they had started a political and military chain reaction (the nuclear arms race) that could eventually destroy the world—a fear that haunts the film's ending.

Lewis Strauss was a founding commissioner of the Atomic Energy Commission and a major political figure.

He held a personal grudge against Oppenheimer due to perceived slights and ideological differences. He orchestrated the 1954 security hearing that stripped Oppenheimer of his clearance, effectively ending his government career.