What is legally required of the perpetrator, in terms of public and private rights, in the case where he accidentally killed his mother with a gunshot, and everyone involved pardoned him for it?

In this case, the blood money (Diyyah) and expiation (Kaffarah) are obligatory. The blood money is incumbent upon the 'Aqilah (the male relatives on the father's side), and the killer is one of them, but he does not inherit anything from it; rather, he inherits from his mother's wealth. The blood money is waived if the heirs pardon it. The expiation is the freeing of a believing slave; if one cannot find one, then it is fasting for two consecutive months.