Transcribing would be the act of sitting down and writing the notes and rhythms you hear, This is a pretty standard practice and how we learn songs. This can get difficult to do with a completed piece of recorded music as parts bleed together and effects can obfuscate notes. It is a little different if you want to "reverse engineer" the ...
Transcription: Is the process of listening to a piece of music and "reverse engineering" it. It can also mean just the process of writing down a piece of music.
You'll find a number of questions on this site related to transcription. As a starting point, just search for the word "transcribe" or for the transcription tag.
It's common in the European music theory to refer to chromatic signs in the key signature simply as key signature signs. The chromatic signs that are not in the key signature are accidentals OR signs of alteration.
The term you may be looking for is recitative.
Recitative is intended to follow the accents and rhythms of normal speech. In this way it sounds less like a melody and more like a musical conversation in the middle of a scene. It's often used to move the drama forward in an opera (by presenting important new information, etc.), but this isn't always the case.
It means they expect the musical choices to display different aspects of piano technique.
For example, the Level 3 list (page 35) contains
"Arabesque" by Johann Burgmüller (SCORE)
"Allegro in A Major" by Johann Hässler (SCORE)
"Morning Prayer" by Cornelius Gurlitt (SCORE)
"Arabesque" and "Allegro" are ...