Actually I do know why he did it. Because in order to notate the C natural as such, He would have had to put a natural sign in front of the C. Later in the same measure, C# is needed. It is less confusing to use a B# than putting a bunch more naturals and sharps all over the place. I hope that made sense
This piece is written in C# minor. The scale of C#minor has exactly the same notes as the scale of E major, hence the identical key signature (F#, C#, G#, A#). It goes: C# - D# - E - F# - G# - A# - B - C#
Your explanation is correct to almost the slightest detail, and is very comprehensive... However, you did make a small mistake. The identical key signature that C#m and E have is (F#, C#, G#, D#), there is no A# included. There is therefore no need for an Ax (A double sharp) when the submediant note is sharpened.So the C#m scales are:NaturalC# - D# - E - F# - G# - A - B - C# (ascending and descending)HarmonicC# - D# - E - F# - G# - A - B# - C# (ascending and descending)MelodicC# - D# - E - F# - G# - A# - B# - C# (ascending)C# - B - A - G# - F# - E - D# - C# (descending)I'm not trying to be mean - just helpful.