What is the meaning of "va'Yiten Osah Lemartah Lispos ba'Kaf"?
Rashi: The staff was given to be polished and proper to hold in the hand.
Radak: Lemartah is Makor (infinitive) with an added Hei, like "Lekarvah El ha'Melachah" (Shemos 36:2). This is why there is no Dagesh in the Hei (it is not a pronoun). Hashem, who removed it from its case, gave it to be made shiny, so the murderer will hold it in his palm after it is made shiny.
Refer to 21:15:5:4-5.
What is the significance of "Hi Huchadah Cherev [v'Hi Moratah Lases Osah b'Yad Horeg"?
Rashi: This staff is the sharp, polished sword to give to Nebuchadnetzar, to kill with it.
Radak: The matter is repeated. It should say Hi Cherev Huchadah; the words are reversed, like "Kol Rabim Amim" (Tehilim 89:51) is like Amim Rabim; "Rabos Itim" (Nechemyah 9:28) is like Itim Rabos.
Malbim (according to the Nimshal): This hints to Nebuchadnetzar's siege of Yerushalayim. Had there not been quarrels and war among Yisrael, he could not have conquered it. However, they fought each other, and there was war between the king, nation and factions ? "Hineni Mesev Es Klei ha'Milchamah Asher b'Yedchem Asher Atem Nilchamim Bam Es Melech Bavel? v'Asafati Osam El Toch ha'Ir ha'Zos" (Yirmeyah 21:4), "Lo He'eminu Malchei Eretz? Ki Yavo Tzar v'Oyev b'Sha'arei Yerushalayim; me'Chatos Nevi'eha Avonos Kohaneha ha'Shofechim b'Kirbah Dam Tzadikim" (Eichah 4:12-13). Via killing each other, Nebuchadnetzar was able to conquer them 1 . Nebuchadnetzar was crafty to sharpen one side of his sword, and dull the other; it was just to scare them. He acted as if he slackens from war and seeks to make Shalom with them.
Malbim: The same applies to Churban Sheni via Edom. Titus saw that he cannot conquer it. When he began to fight against the wall, all factions (in Yisrael) united against him and killed Romans. He went away, and the factions fought and killed among themselves. Also Nebuchadnetzar saw this; he departed from the siege in the middle, and via this Yisrael were divided and killed each other.
