Is it permissible for a Muslim to fortify himself by reciting the Basmalah and Surat Al-Ikhlas while specifying the six directions, and does this include saying "from beneath me"? And was the prostration mentioned in the story of Joseph by his parents? And is it permissible for a Muslim to repeat specific verses of the Quran of his own choosing with the intention of healing and fortification?

It is permissible to perform Ruqyah with the supplication mentioned in the question, for something similar has been narrated, elevated to the Prophet, peace and blessings be upon him, though some scholars have deemed it weak. However, it does not contain any forbidden elements, and its meaning is good. There is no objection to saying: "And from beneath me." Similarly, there is no objection to mentioning specific verses from the Quran and using them for Ruqyah, for the entire Quran is a healing. The Lawgiver has permitted Ruqyah as long as it does not involve polytheism (shirk). Scholars have unanimously agreed on the permissibility of Ruqyah using verses and remembrances of Allah the Almighty.