Short answers, pulled from the story.
Ludwig Ritter von Köchel (1800-1877) was an Austrian musicologist, botanist, and private scholar who published the Köchel catalogue in 1862. He is famous for cataloguing all of Mozart's known works and originating the KV-numbers (Köchel-Verzeichnis) by which those works are universally identified.
The Köchel catalogue, published in 1862, is a chronological and thematic register of the works of Wolfgang Amadeus Mozart. It was the first catalogue of any composer produced on such a scale and with such scholarly rigor, and it has undergone revisions since its original publication.
KV stands for Köchel-Verzeichnis, the German name for the catalogue Ludwig Köchel created. Mozart's works are referred to by their KV-numbers in the same way other composers' works carry opus numbers; for example, the Jupiter Symphony is KV. 551.
Köchel studied law in Vienna and graduated with a PhD in 1827. For fifteen years he worked as tutor to the four sons of Archduke Charles of Austria. After that service he received a knighthood and a financial settlement that allowed him to pursue scholarship independently.
Otto Jahn was independently assembling a comprehensive collection of Mozart materials and writing a scholarly biography of Mozart at the same time Köchel was compiling his catalogue. When Jahn learned of Köchel's project, he turned his collection over to Köchel, who dedicated the finished catalogue to him.
Köchel conducted botanical research in North Africa, the Iberian Peninsula, the United Kingdom, the North Cape, and Russia, earning admiration from contemporary scientists. He was also interested in geology and mineralogy, and he catalogued the works of the composer Johann Fux.