Short answers, pulled from the story.
Hummel studied with Wolfgang Amadeus Mozart, who taught and housed him free of charge for two years beginning at age eight. He later received instruction from Muzio Clementi in London, and upon returning to Vienna was taught by Johann Georg Albrechtsberger, Joseph Haydn, and Antonio Salieri.
Hummel influenced Chopin directly through his piano concertos, which Chopin kept in his active performing repertoire. His twenty-four preludes, Op. 67 (1815), are widely seen as a precursor to Chopin's Preludes, Op. 28. Liszt was shaped indirectly through Carl Czerny, who transferred to Hummel after studying with Beethoven and later taught Liszt.
Haydn appointed Hummel as Konzertmeister at Nikolaus II, Prince Esterházy's estate at Eisenstadt in 1804. He took on Kapellmeister duties while Haydn's health declined, but only received the Kapellmeister title after Haydn died in May 1809. He was dismissed in May 1811 for neglecting his duties.
Hummel published A Complete Theoretical and Practical Course of Instruction on the Art of Playing the Piano Forte in Germany in 1828. It sold thousands of copies within days of publication and introduced a new approach to fingering and the playing of ornaments that spread through European piano teaching.
Hummel died famous in 1837, but his classically balanced style and Clementi-derived technique were seen as old-fashioned as Romantic bravura took hold. He was further overshadowed by Mozart and Beethoven. His reputation was not revived during the early twentieth-century classical revival, and his rediscovery came through a later increase in recordings and live performances.
Schubert's friend Albert Stadler stated that the Trout Quintet was modelled on the quintet version of Hummel's Septet in D minor for Flute, Oboe, Horn, Viola, Cello, Bass, and Piano, Op. 74. Schubert's Quintet in E-flat, Op. 87 may have been a further influence.