Short answers, pulled from the story.
The Van Allen radiation belt is named after James Van Allen of the University of Iowa, who published an article describing the belts in 1958. The existence of the belts was confirmed by the Soviet satellite Sputnik 2 and the American satellites Explorer 1 and Explorer 3 in early 1958.
Earth's two main Van Allen belts extend from an altitude of about 640 to 58,000 kilometers above the surface. The inner belt spans roughly 1,000 to 12,000 kilometers up, while the outer belt reaches from about 3 to 10 Earth radii.
Apollo astronauts did pass through the Van Allen belts, but received a very low and harmless dose of radiation because spacecraft traveled at high speeds through the thinner upper portions of the outer belt. The Apollo 14 mission was the exception, traveling through the heart of the trapped radiation belts.
Project Argus was a 1958 US program that detonated low-yield nuclear bombs at an altitude of 300 miles to test whether nuclear explosions in space could release enough trapped electrons to disable intercontinental ballistic missile warheads. The project was discontinued due to the atmospheric testing treaty and concerns that the added radiation could interfere with the Apollo moon missions.
A transient third radiation belt was confirmed on the 28th of February 2013 by NASA's Van Allen Probe team. It was triggered by a coronal mass ejection from the Sun and persisted for about four weeks before merging back into the outer belt.
The Van Allen belts do confine antiprotons, confirmed in 2011 by the PAMELA experiment while passing through the South Atlantic Anomaly. The energy of the detected antiprotons ranged from 60 to 750 MeV, though the total quantity across the entire belt is estimated at only about 10 micrograms.