K often refers to Kochel numbers, which is a means of cataloging all of Mozart's works done by Ludwig von Kochel. Instead of opus numbers, each piece is assigned a K number by order of composition. An example would be Piano Concerto No. 23, K. 488.

Most likely Mozart ... especially since the letter "k" is in the question. "K" stood for Koechel, the person who cataloged every piece Mozart wrote and assigned each composition its own unique number.

Which composer? Mozart's concerto no. 23 in A has its second theme in E major, and in the recapitulation it returns in A major. Schumann's concerto in A minor has its second theme in C major, returning in A major for the recapitulation.

There is no such concerto. Mozart wrote several piano concertos in C major, among which the famous KV 467 (Piano conc. no 21). KV 333 is a piano sonata in B flat major.