Is it permissible to watch children's channels and programs that contain music if the origin of these films and programs is not the music itself, and is it permissible to lower the television volume completely to watch them?

If movies are free of prohibitions except for music, then there is no harm in muting or disabling it because the illah (legal cause) is the act of listening (sama’). Listening to music is not permissible and its prohibition is fundamental. There is a difference between one who intentionally listens and one who is forced to hear. The one who is forced is excused, just as the Prophet, peace and blessings be upon him, and Ibn Umar did by placing their hands over their ears when they heard the sound of the zammarah (flute), seeking what is better and more complete. Commands and prohibitions relate to intentional listening (istima), not merely unintentional hearing (sama’).