1)
What is the meaning of "Alai Adoni ha'Melech he'Avon
1.
Rashi: This is a euphemism. Really, she meant that if I go home, and you do not command, and my son is killed, the sin will be on you!
2.
Malbim: A king may punish unlike Torah law for a need, e.g. murder of a stranger. Here, one killed his brother. No one will learn from this to do similarly! Therefore, the king is exempt from investigating whether he must use his power here to punish.