To what extent is the supplication authentic: "O Allah, I ask You by the Throne, and the Footstool, and the light upon which our Master Muhammad, peace and blessings be upon him, is, that You subdue for me the heart of whomever You have made me dependent upon, and that You protect me from the evil of one who has power over me, and over whom I have no power"?

It is not permissible to seek intercession through the Throne (Al-Arsh) and the Footstool (Al-Kursī), as seeking intercession through created beings is forbidden and a reprehensible act (makrūh taḥrīman) according to the Salaf. It is considered haram by Ibn ʿUthaymīn. It is also not permissible to seek intercession through the Prophet Muhammad, peace be upon him, so it is even more impermissible to seek intercession through the Throne and the Footstool.

As for seeking intercession through "the light that is upon Muhammad, peace be upon him," it is permissible if what is meant by it is the Holy Qur'an, due to the Almighty's saying: "So believe in Allah and His Messenger and the light which We have sent down" (64:8). However, if what is meant is the light of the Prophet, peace be upon him, himself, then it is not permissible, because it is a created thing.