What is the meaning of "Agag Ma'adanos"?
Rashi citing Targum Yonasan: The graceful Agag. Radak - i.e. he went like kings go amidst indulgence. Even though he was close to death, he went haughtily. Or, he went happily, for he chose (preferred) his death over his life.
Radak: Agag from his fetters and iron chains. This is like "Haskasher Ma'adanos Kimah" (Iyov 38:31)
What is the meaning of "Achen Sar Mar ha'Maves"?
Rashi: I know that Sar (turned) and is close to me Mar (the bitterness) of death.
Eichah Rabah 3 (Tashiv): (Shmuel was cutting up Agag. Agag said,) do we give such bitter death to nobles?!
Chomas Anach citing R. David Melamed #1: In addition to death itself, there is extra bitterness if a commoner will kill him. He understood that Shmuel will kill him, so this bitterness departed. 1
Chomas Anach citing R. David Melamed #2: Bitterness of death is to die childless. He knew through witchcraft that his wife is pregnant, and he saved her via witchcraft. The bitterness departed, for he will leave evil seed. Haman came from him! Chomas Anach - he was consoled that Amalek will not be wiped out. It has the same Gematriya as "Mar".
Malbim: "Mar" is like Yamir (exchange for), like the first Mar in "l'Shalom Mar Li Mar" (Yehoshua 38:17). Now [after being captured] I live amidst disgrace and slavery, in exchange for (in place of) death. Nobles prefer death to this!
