Is it better to go to prayer upon hearing the Adhan, even if a sin results from that in the place one left, or to stay in the place to prevent the sin and delay the prayer, and until when can the prayer be delayed in this situation?

A general ruling cannot be given for the conflict between benefit and harm. The principle in this regard is that warding off harm takes precedence over acquiring benefit, unless the benefit outweighs the harm. So, if a Muslim knows that a murder will occur if he goes to the mosque, it is not permissible for him to go, and he should pray in his place, because preserving life is greater than the benefit of congregational prayer. However, if the benefit of congregational prayer outweighs the harm, such as listening to songs, then he should be advised, and then he should go to the mosque.