Is it permissible for a righteous man to write the Qur’an for a sick person to heal him, and is it permissible to hang these verses around the neck?

Writing verses for treating the sick is not permissible, whether by hanging them or writing them on the body. What is permissible is reciting the verses, blowing (over the patient), and supplicating for the sick, and this is part of the lawful ruqyah. There is no harm in reciting the Quran over water and then drinking it. However, hanging verses or any other amulets is not permissible, due to the Prophet's (peace be upon him) saying: "Whoever hangs an amulet, may Allah not fulfill his need; and whoever hangs a seashell, may Allah not grant him peace."