If the music causes ‘tarab’ then it is not permissible to listen to it. ‘Tarab’ means the psychological interaction with the music or singing, whether it leads to joy, sadness, pride or any other emotion.
We cannot confirm that an Imam has recited this supplication. Yes, it has been reported in some books that the said supplication is narrated by one of the Imams (peace be upon them). Supplicating to Almighty Allah by the Prophet or the Imams (peace be upon them) is amongst the recommended deeds even if it was by other than this particular supplication.
It is permissible for the man and woman to pray next to each other, although it is disliked. Such dislike can be avoided when the position of the man is ahead of the woman, in such a way that when she prostrates her forehead would be adjacent to his knees. It is better that the man's position is ahead of that of the woman's by a distance of a step.