What are the specific supplications for healing (du'a al-shifa) for the sick, and what do the patient's family members say on their behalf in case they are unable to supplicate or perform Ruqyah themselves?

The ruqyah according to Sharia is a means of healing, by the will of Allah Almighty. The best cure is the Book of Allah, especially Al-Fatiha and Al-Mu'awwidhatayn (the two chapters of refuge), though the entire Qur’an is a healing. Among the authentic prophetic supplications are: “O Allah, Lord of mankind, remove the affliction and grant healing. You are the Healer. There is no healing but Your healing, a healing that leaves no illness behind.” And placing the hand on the site of pain and saying "Bismillah (in the name of Allah)" three times, and "A'udhu billahi wa qudratihi min sharri ma ajidu wa uhadhiru (I seek refuge in Allah and His power from the evil of what I find and what I fear)" seven times, and the supplication "Rabbuna Allahu alladhi fi as-sama'i taqaddasa ismuka… (Our Lord Allah, Who is in the heaven, hallowed be Your Name…)." One can refer to reliable books of supplications such as Sahih Al-Kalam At-Tayyib and Hisn Al-Muslim.