What is the ruling on believing and following the authentic (sahih) hadith, the authentic due to external factors (sahih li ghayrihi), the good (hasan) hadith, the good due to external factors (hasan li ghayrihi), the weak (da'if) hadith, and the very weak (da'if jiddan) hadith, with a request for evidence from the Qur'an and the Sunnah? And does one who follows a hadith mentioned by Bukhari or Muslim, which they declared "authentic" (sahih), but it is not so due to their error, receive a reward, like the hadith "Whoever honors his parents, Allah will prolong his life," if it was falsely attributed to the Messenger?

The prophetic Hadith is either accepted (authentic or good) or rejected. The accepted Hadith must be acted upon if it is free from contradiction and abrogation. What is in the Two Sahihs (Bukhari and Muslim) is accepted by the Ummah by consensus. The evidence for acting upon the accepted Hadith is abundant from the Qur’an and Sunnah, such as His (Allah’s) saying: "And whatever the Messenger gives you, take it," and "Obey Allah and obey the Messenger." The one who acts upon thentic Hadith is rewarded, and obedience to the Messenger is a cause for entering Paradise. As for the Hadith you mentioned in the example, it is weak, and a weak Hadith is not acted upon in matters of creed, lawful, or unlawful. It is permissible to act upon it in matters of virtuous deeds with certain conditions. There is no fabrication against the Messenger of Allah, peace and blessings be upon him, in Bukhari.