Nico Muhly is actually an American contemporary classical music composer, and plays himself in this episode. He wrote the "Amy Fisher" piece himself, and it was performed here by Ana María Martínez.
The German song that Alessandra sings in the closing scene is Schubert's "Die junge Nonne" (the young nun). The lyrics describe a storm and love: the nun's love is supposed to be for Christ, to whom she is promised as a bride, but the storm represents her conflicting love for the world, which her vocation requires her to renounce, versus her love for Christ. The song dramatizes Alessandra's struggle between loving her art and her attraction to Rodrigo, as well as hinting at the love triangle being set up between Rodrigo, Hailey, and Alessandra.
Danny mentions to Thomas that his mother "saw you do Mahler's Sixth in San Francisco" and it changed her life. This is a reference to Michael Tilson Thomas, music director of the San Francisco Symphony, who was famous for promoting Mahler's music. MTT recorded Mahler's complete orchestral works with the SFS, and his album of Mahler's Symphony No. 6 won the Grammy for Best Orchestral Performance in 2003.