I hope that this harmonic analysis of Ludwig van Beethoven's Piano Sonata Op. 2 No. 1 first movement will help you in your work. I will try my best to post the second movement as well as soon as possible. If you are interested to find out something about stylistic procedures in this musical piece, please let me in the comments.
The non-diatonic chords are the chords that do not appear in one particular key naturally. These non-diatonic chords on the II scale degree are quite important for the overall musical expression. As you shall see, some of them can appear only in Major keys and some of them are more characteristic for minor keys.
Enharmonic modulation is one of the most important and most powerful tools in music. In this article you can learn everything you need to know about it.