To what extent is the hadith authentic which mentions that a Bedouin asked the Messenger of Allah, peace and blessings be upon him, about guaranteeing Paradise in exchange for only the five daily prayers and fasting, whereupon the Messenger answered him in the affirmative on condition of prolonging prostration, because it is a burning for Iblis?

The style mentioned in the question does not resemble the style of the Prophet, peace be upon him, and the clumsiness of the style is one of the indications that the hadith is fabricated. It is established that abundant prostration is a cause for entering Paradise, as in the hadith of Rabi'a al-Aslami: "Help me achieve this for yourself by prostrating frequently." It is also established that performing the obligatory duties and avoiding the forbidden enters one into Paradise, as in the hadith of Nu'man ibn Qawqal, who asked: "Tell me, if I perform the prescribed prayers, deem forbidden what is forbidden, and deem lawful what is lawful, will I enter Paradise?" The Prophet, peace be upon him, replied: "Yes."