Is what the healer did — using incense and papers containing incomprehensible letters and numbers — considered charlatanry, and will I be sinful if I burn them, knowing that I was in need of treatment and the healer claimed he used the Quran?

Treatment with ruqyah (incantations) and supplications is permissible if they involve the remembrance of Allah and are understandable, because what is not understood cannot be guaranteed to be free of polytheism (shirk). When Imam Al-Shafi'i was asked about ruqyah, he permitted it with the Book of Allah and with what is known from the remembrance of Allah. He also permitted the ruqyah of the People of the Book for Muslims if it was with what is known from the Book of Allah and His remembrance. However, unknown and incomprehensible names, such as "Ya Azran, Ya Kayan," are not permissible for ruqyah. Therefore, if there is anything in theq ruqyah whose meaning is not understood, it is not permissible to believe the practitioner; rather, one must stay away from him and turn to Allah through prayer and supplication.