Short answers, pulled from the story.
Mozart's piano concertos are numbered from 1 to 27, with three additional unnumbered arrangements, K. 107/1, 2 and 3. Of the twenty-seven, the first four are orchestrations of other composers' works, and twenty-one are original compositions for solo piano and orchestra.
Most of Mozart's original piano concertos were written for his subscription concert series in Vienna between 1784 and 1786. In that period alone he composed eleven concertos. These include the D minor K. 466, C major K. 467, A major K. 488, and C minor K. 491.
The nickname 'Elvira Madigan' belongs to Mozart's Piano Concerto No. 21 in C major, K. 467. Bo Widerberg's 1967 Swedish film used the concerto's slow movement so extensively that the nickname has outlasted the film itself. The film is today largely forgotten.
In the nineteenth century, only the two minor-key concertos were regularly performed. These were No. 20 in D minor, K. 466, and No. 24 in C minor, K. 491. Clara Schumann first performed K. 466 in 1857 and K. 491 in 1863; they remained the standard Mozart concerto repertoire for decades.
Mozart performed his mature piano concertos on a fortepiano, not a harpsichord; his preferred instruments were those built by his friend Stein and by Anton Walter. His original fortepiano returned to Vienna in 2012 after a two-hundred-year absence, and was played in a concert shortly after.
The Jenamy concerto is Mozart's Piano Concerto No. 9 in E-flat major, K. 271, composed in January 1777. Its most striking feature is a structural irregularity: the piano interrupts the orchestral opening after only one-and-a-half bars. Scholars regard it as one of Mozart's early masterpieces and a decisive advance in his approach to the concerto form.