1)
Why should Shlomo swear today?
1.
Malbim: The custom is that kings pardon transgression on the day they become king, for it is a day of Chesed. Therefore, he should swear today, especially since I was immediately submissive [to him].
2)
Why did he say "Im Yamis Es Avdo be'Charev"?
1.
Radak: I am afraid and unsure about this. Let him swear not to kill me!
2.
Malbim: A king may kill only via the sword. He should swear] not to kill me for my rebellion.