Is teaching children music and religious and national singing, and playing the organ for that purpose, permissible or forbidden? Is working in a religious chanting group permissible or forbidden? What is the ruling on musical instruments? And should one leave the work if it is forbidden?

The use of musical instruments is Haram (definition) (forbidden) by consensus, except for the drum (Duff) for women during the two Eids and celebrations, based on the Prophet's (peace be upon him) saying: "There will be people from my Ummah who will consider lawful adultery, silk, wine, and musical instruments." What you mentioned about religious and national songs does not justify the use of musical instruments. You are obligated to abandon this work unless you are compelled to it to the point of perishing, in which case you may remain in it until you find an alternative.