Are the following Hadiths authentic: [A mouse came and began dragging a wick, which it then threw between the hands of the Messenger of Allah, peace and blessings be upon him, onto the mat he was sitting on, burning an area the size of a dirham from it] and [A group of people came to the Messenger of Allah, peace and blessings be upon him, and said, "We have a ship at sea that needs oil. We found a dead she-camel with much fat; may we oil it with its fat?" He, peace and blessings be upon him, replied, "Do not benefit from anything from a dead animal"]?

The first Hadith (definition), about extinguishing lamps when going to sleep, was narrated by Abu Dawud, Ibn Hibban, Al-Hakim, and Al-Bayhaqi with the wording: "A mouse came... So the Prophet, peace and blessings be upon him, said: 'When you go to sleep, extinguish your lamps, for Satan guides the likes of these (mice) to this (fire) and they burn you.'" This Hadith was authenticated by Al-Hakim, Al-Dhahabi, and Al-Albani.

As for the second Hadith, concerning benefiting from a carcass, it was narrated by Ibn Wahb, Al-Tahawi, Al-Shaybani, Abu Al-Shaykh, and Ibn Abd al-Barr from Zam'ah ibn Salih, from Abu Al-Zubair, from Jabir. Some imams considered Zam'ah weak, but Ibn Adi said that his Hadith is acceptable and there is no harm in it. Ibn Qudamah graded it as hasan (definition) (good) in "Al-Mughni." It is supported by the Hadith of Abdullah ibn Ukaym, narrated by Ahmad and the compilers of the Sunan, and authenticated by Al-Albani: "Do not benefit from a carcass, neither its skin nor its sinews."