Short answers, pulled from the story.
Franz Liszt was Czerny's most famous pupil, taught free of charge from 1819. Other notable students included Theodor Leschetizky, Theodor Döhler, Theodor Kullak, Stephen Heller, Anna Sick, and Ninette de Belleville, whose own pupils extended Czerny's influence to Sergei Prokofiev, Wanda Landowska, Daniel Barenboim, and Van Cliburn.
In 1801, the Czech composer and violinist Wenzel Krumpholz arranged a presentation for the ten-year-old Czerny at Beethoven's home. Beethoven asked Czerny to play his Pathétique Sonata and the song Adelaide, was impressed, and accepted him as a pupil. Czerny studied under Beethoven until 1804, with sporadic lessons after that date.
Czerny composed more than one thousand works, extending to Opus 861. His output included piano études, nocturnes, sonatas, variations, masses, symphonies, string quartets, and choral pieces. The majority of the works he considered serious music remain in unpublished manuscript form at Vienna's Society for the Friends of Music.
Liszt published his twelve Études d'exécution transcendante in 1852 with a dedication to Czerny. Czerny had taught Liszt free of charge from 1819, when Liszt's father brought the boy to him, and Liszt repaid this early support by performing Czerny's music at his Paris recitals and through the dedication.
Czerny was the first person to report symptoms of Beethoven's deafness, several years before the matter became public knowledge. At their first meeting in 1801, Czerny noticed cotton in Beethoven's ears that appeared to have been steeped in a yellowish ointment. He recorded this observation in his autobiography and letters.
Czerny, who never married and had no close relatives, willed his large fortune to charities including an institution for the deaf, to his housekeeper, and to the Society of Friends of Music in Vienna. He also made provision for a Requiem mass to be performed in his memory. The Society of Friends of Music holds the unpublished manuscripts of his serious music to this day.