Is the aforementioned hadith regarding Adam's asking his Lord by Muhammad (peace and blessings be upon him) and God's forgiveness of him authentic?

This hadith is fabricated and false. Al-Dhahabi, Al-Hafiz Ibn Hajar, Al-Bayhaqi, and Al-Albani all critiqued Al-Hakim's authentication of it, emphasizing the unanimously agreed-upon weakness of its narrator, Abd al-Rahman ibn Zayd ibn Aslam, and his accusation of fabricating hadiths.