Like most musicians, sometimes I sit down and listen to a song, and attempt to "reverse engineer" what the notes and chords and so on might be.
Is there a widely understood term for that?
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.
EDIT: Transcription is different from copying, as pointed out by Dekkadeci in the comments. "Copying" is the act of literally transferring one sheet of notated music to another. "Transcribing" requires writing down a sound that was not previously written: from a recording, from nature, by re-writing notated music for one or more instruments other than in the given notation.
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 engineering and production of the finished piece. At the end of the day the starting point is your ear, a well trained ear could determine if there is chorus, delay, etc added to the instruments.
In addition to your ear there are software packages that apply signal processing techniques to try and separate the individual notes in a small time window of the entire piece of music. This can be a helpful aid if you cannot figure something out but it's still transcribing.