Does working on a website to earn money, which requires running a special program on the device 24 hours a day, affect the lawfulness of the money earned from it, given the possibility of performing congregational prayers, and does listening to music affect this money?

You must pray in congregation, and the duration of the prayer is excluded from the rental period. Your going to the congregation does not affect the lawfulness of your money, and you must perform the work for which you were hired to the fullest extent, bearing in mind that listening to music is forbidden.