Taike,
If I understand your post, you are asking about the notes and chords that are written in a fake book. Do I change or add to the melody, and do I change or add to the chords that are written.

I have a background in improvisation and re-harmonizing, so when reading from a fake book I take each chord and reduce it to it’s simplest form. G13 to G7 – Am11 to Am. From there I recreate based on what I have learned.

EX. G7 chord for three measures going to a C chord.
G7 C—Original
1- Dm7 G9 CMaj7
2- Dm7 G7-9 C6
3- Dm7 Db7 C6/9
The song can be made to flavor any type of music. I remember being given an assignment of re-harmonizing Twinkle Twinkle Little star –the song became an involved Jazz creation.

Melody
In the melody there are important notes and notes that add to those important notes – these notes are leading to or away from the important ones, – I keep the important, and if it feels right add what I am feeling. When I am done it is John, not the best in the world, and it has my flavor. The same song is not always played the same.

IMHO, John C.