Is it permissible to utter the Name of Majesty (Allah) or some verses while listening to forbidden music, and is it obligatory to turn off the television if music plays on it during prayer or the Adhan?

It is not permissible to listen to singing that includes musical instruments. The television must be turned off when such music is playing. This prohibition is further emphasized when the name of Allah is mentioned, or the Quran is recited, or the Adhan (call to prayer) is heard. Mixing music with the remembrance of Allah is even more forbidden. This question is not among the forbidden questions, for the forbidden questions are those from which there is no benefit, no action results, and they might harm the questioner.