The first video is of Arcadi Volodos' version of the Alla Turca section of Mozart's Piano Sonata no. 11 in A Minor. I posted it rather than the original because everybody has heard the original too many times (no offense, Mozart). It's a continuation of the impulse to write the hardest possible pieces for piano, for which Volodos (the pianist in the above video) is known--nobody else can play that piece with the same precision and vigor, which is exactly why he wrote it. He wrote a version of Mendelssohn's wedding march in similar style.
The second piece is the "Turkish March" from Beethoven's incidental music to The Ruins of Athens. It is also very well-known and written in even more typically Janizary style; you can clearly hear the percussion accompanying the "band."