How can one rid oneself of the rights of those who have been backbitten, whether directly or by listening to one's father curse heads of state? Is it sufficient to supplicate for them with a feeling of distress? And are the two rak'ahs of repentance obligatory in this case?

The expiation for backbiting is by seeking forgiveness for the person you backbit, mentioning their good qualities, and supplicating for their forgiveness. Your father should be advised gently and kindly. It is recommended for both the backbiter and their father to perform the prayer of repentance, which consists of two rak'ahs after purification and seeking forgiveness, and it is mentioned in the hadith that it is a cause for forgiveness.