The first one is “My Heart Ever Faithful” by J.S. Bach (and she threw in an aeolian flux…). The ballet, I do not know, but it would’ve been nice had the orchestra tuned first (um…..and the harpist too on the Bach come to think of it….)
If the ballet you are referring to is the Ballet SM on youtube, with the little girls, the music is the Dance of the Hours from the opera La Gioconda by Ponchielli.