If you want to save songs that you added with the Quick Add button during a performance, you can turn on Settings > General Settings > Save Quick Added Songs.
There is no way for the app to know if you played the songs in a different order than the set list, unless you actually edit the set list during your performance, in which case those changes would always be saved.
To remember songs you did not play, you could edit your layout and turn on the Song Number option, then check off the songs as you play them, then go back after the show and remove the songs that you didn't play.