1)
What is "Mishpat ha'Meluchah"?
1.
Radak: It is the king's rights over the nation, like written above 8:11-17.
2.
Malbim: This is not Mishpat ha'Melech (8:11-17), which is what he enacts by force. Mishpat ha'Meluchah is what is proper for the king's honor and fear, according to Torah law; this was written in the Sefer.
2)
What is "Lifnei Hashem"?
1.
Radak: It is in the Aron.