What is the ruling on turning off the radio when hearing the voice of a Qur’an reciter who is not engaging, and what is the ruling on some reciters embellishing the Qur’an with melodious chanting and the listeners saying "Allah" and "Ya Salam 'Alayk Ya Shaykh" after every verse?

What your friend did is wrong, because the Quran is listened to because it is the Quran, not because it is in the voice of so-and-so. And beautifying one's voice when reciting the Quran is مطلوب [desirable/commanded], as long as it does not exceed its limit and become like musical tunes.