Are the supplications mentioned in the question sound and authentically reported in the Prophetic Hadiths, or are they merely personal experiences which it is permissible to act upon?

There is no harm in reciting the Quran for the fulfillment of a need, but specifying a certain number of recitations or times for it has no evidence and may contradict the Sunnah. Specifying acts of worship without evidence is considered an innovation (bid'ah). The use of words or supplications of unknown meaning in ruqyah is prohibited, for fear that they may be disbelief (kufr) or unlawful according to Sharia. What is sanctioned by the two revelations (Quran and Sunnah) is permissible, but what has unknown meanings may be a satanic whispering, and perhaps even disbelief or sorcery.