What is the ruling on speaking an incomprehensible language in prayer and supplication, and claiming that it is a miracle (karamah) for healing the envious and expelling jinn? And is there a miracle (karamah) called "the miracle (karamah) of the People of the House (Ahl al-Bayt)"?

There is no evidence for a special "dignity" (karamah) for the Ahl al-Bayt. Ali ibn Abi Talib himself denied that the Prophet, peace and blessings be upon him, singled them out in any way above other people. Furthermore, ruqya (exorcism) and treatment for jinn and envy using incomprehensible words are forbidden. One must restrict oneself to ruqya with the Qur'an and the reported supplications. Scholars disliked any ruqya that was not by the remembrance of Allah and His names specifically, and in the Arabic language whose meaning is understood, because it could be shirk (definition) (polytheism) or magic.