Short answers, pulled from the story.
James Van Allen published an article describing these belts later that year in 1958. Explorer 1 sent back data in early 1958 that changed our understanding of space before this publication.
The inner belt extends from an altitude of 0.2 to 2 Earth radii above the surface. The South Atlantic Anomaly allows the inner boundary to drop to roughly 200 km above Earth due to the offset of the belts from Earth's geometric center.
NASA announced the discovery of a transient third radiation belt on the 28th of February 2013. This layer persisted for four weeks before merging back into the traditional outer belt as a product of coronal mass ejection from the Sun.
Only the Apollo 14 mission traveled through the heart of the trapped radiation belts. Astronauts received very low and harmless doses due to the short time spent flying through them while other missions minimized hazards by sending spacecraft at high speeds.
Antiproton energy was measured between 60 and 750 MeV during the 2011 detection. Levels of antiprotons were orders of magnitude higher than expected from normal particle decays while passing through the South Atlantic Anomaly.