FAQ for
The Quiet (2005) More at IMDbPro »

Camilla Belle (Dot) played almost all of them herself:

(When Dot first sees the school piano) - Beethoven: "Piano Sonata #28 Opus 101, Andante ma non troppo, con affecto"

(when Connor interrupts Dot with the lab question)- Beethoven: "Piano Sonata #26 Opus 81a, 'Les adieux', Adagio"

(when the piano string breaks)- Beethoven: "Piano Sonata #23 Opus 57, 'Appassionata', Allegro assai"

(during Nina and Paul's confrontation) - Beethoven: "Piano Sonata #14 Opus 27, No. 2 'Moonlight', Adagio"

(ending and credit scroll) - Beethoven: "Piano Sonata #19 Opus 49, No. 1, Andante"

No, though it is implied for both in several sexual scenes, nothing is shown. Edie Falco (Olivia Deer) goes topless for a minute or so in one scene.