Short answers, pulled from the story.
Hessel Gerritsz (c. 1581-1632) was a Dutch engraver, cartographer, and publisher regarded by some as unquestionably the chief Dutch cartographer of the 17th century. He was the first exclusive cartographer of the Dutch East India Company (VOC), appointed on the 16th of October 1617, and produced some of the most influential maps of Australia, the South Pacific, and the Americas of his era.
Gerritsz published a Dutch translation in Amsterdam in 1612 whose title page contains the phrase "Land ghenaemt Australia Incognita," believed to be the earliest occurrence in print of the word Australia outside Spain. His 1612 world map and subsequent publications were also influential in establishing the name Australia more broadly.
Gerritsz was appointed the first exclusive cartographer of the VOC on the 16th of October 1617, on recommendation of Petrus Plancius, chief scientist of the VOC. All charts and logs from returning VOC merchants and explorers had to be submitted to him, and his maps accompanied every VOC captain on their voyages. He held the post until his death in 1632.
The first map to show an outline of Australia was produced by Hessel Gerritsz in 1628. It was an update of his 1627 Caert van't Landt van d'Eendracht that added the 1627 charting of Australia's south coast by Francois Thijssen.
Florida appeared as Tegesta on maps because Hessel Gerritsz used that name on his influential map of Florida, which was based on French and Spanish sources. The name remained in use for approximately two hundred years after Gerritsz applied it.
Hessel Gerritsz died in 1632 in Amsterdam, Dutch Republic, and was buried in the Nieuwe Kerk on the 4th of September, aged about fifty.