I’ve heard all of those songs except your #2. However, I [i]am[/i] familiar with Samuel Barber’s Adagio for Strings.
Great recommendations! Here’s what I have to add to your list:
Claire de Lune, by Claude Debussy
Traumerei, by Robert Schumann
La Campanella, by Franz Liszt
“Prelude and fugue” from Johann Sebastian Bach’s “The Well-Tempered Clavier”
Piano Concerto no.2, by Sergei Rachmaminov
Sonata “Pathetique”, by Ludwig van Beethoven