Short answers, pulled from the story.
Amerigo Vespucci published the letter titled Mundus Novus in the spring of 1503. This document contained the first explicit articulation in print of the hypothesis that the lands discovered by European navigators to the west constituted a New World.
The German cartographer Martin Waldseemüller published a map in 1507 that famously labeled the area now called Brazil as America. This name was derived from the feminine form of the Latinized first name of the explorer Amerigo Vespucci, marking the first time the name appeared on a map.
Common beans, maize, and squash were originally domesticated by pre-Columbian peoples in Mesoamerica. Agriculturalists in the Andean region of South America brought forth the cassava, peanut, potato, quinoa, and domesticated animals like the alpaca, guinea pig, and llama.
The western coast of the New World, including the Pacific Ocean, was discovered in 1513 by Vasco Núñez de Balboa. It was a few more years before the voyage of Ferdinand Magellan between 1519 and 1522 determined that the Pacific Ocean definitely formed a single large body of water that separates Asia from the Americas.
Taxonomists attach the New World label to groups of species found exclusively in the Americas, such as New World monkeys, New World vultures, and New World warblers. This biological distinction reflects the long period of isolation that existed between the continents before the Columbian Exchange.