Are the admonitions attributed to Luqman to his son a Hadith from the Messenger of Allah, may Allah's prayers and peace be upon him, and what is its degree if so?

This wording is not a Prophetic Hadeeth. Al-Bayhaqi narrated it in Shu'ab al-Iman from Al-Hasan al-Basri, and Abu Nu'aym narrated it in Hilyat al-Awliya' from Ikrimah as a saying of Luqman. Some scholars have deemed these narrations حسن (good) due to their collective chains of transmission.