What is the ruling of Islamic law regarding a man shaming his wife for her past and constantly questioning her about it, if she has repented from it? What is the proper conduct in this situation? And has any Prophetic حديث (hadith) been narrated concerning this?

It is not permissible for a husband to question his wife about her past, nor is it permissible to reproach a sinner for a sin from which they have repented. The husband should look at his wife's current state: if she is upright, then he should keep her and treat her kindly, in accordance with the Almighty's saying: "And live with them in kindness," and the Prophet, peace and blessings be upon him, said: "The best among you is the best to his family."