"I'm a Dancer!" is "L'amour Est un Oiseau Rebelle" from Bizet's Carmen.
"Piano Lesson 7" is Mozart's "Rondo alla Turca."
"Piano Lesson 8" is Debussy's "Arabesque Nş1."

In FFII, "Temptation of the Princess" is "Finale: Sujet, Andante" from Tchaikovsky's Swan Lake.

In FFIII, "Let's Play the Piano!" is Beethoven's "Bagatelle in A Minor," more commonly known as "Für Elise."