Is listening to music forbidden, even if the listener observes prayer and fasting and does not act upon the implications of the songs, and is this listening considered a sin?

Singing accompanied by music is impermissible (haram), regardless of whether the listener is affected by it or not. If it is free of musical instruments, then listening to it is permissible, provided that it does not contain obscenity or an invitation to anything forbidden by Allah the Almighty.