Why did she say "Yizkar Na ha'Melech
Rashi: Remember - Hashem was adamant to help a Shogeg murderer to reach an Ir Miklat quickly 1 , lest Go'el ha'Dam kill him - "v'Hisigo Ki Yirbeh ha'Derech" (Devarim 19:6), and you reject me (you do not act to protect my son)?!
Radak: Mention Hashem's name and swear 2 [that my son not die], for there are many Go'alei ha'Dam. (If you merely command one, another will kill. If you swear that my son not die, all Go'elei ha'Dam will hear and fear to kill him!)
Radak citing Targum Yonasan: Remember what is written in the Torah of Hashem, to increase the journey (make it hard) for Go'el ha'Dam to kill!
Kli Yakar citing Mahari: Kayin killed Hevel, and Hashem did not want that Kayin be killed, lest destruction increase, and lest Adam's grief be increased. Just the contrary, He made a sign for him, lest animals kill him! Similarly, do not merely say that he will not die - make a sign for me, like Hashem made for Kayin!
Kli Yakar: I fear lest Go'elei ha'Dam demand Kofer, i.e. all my son's money, and then they will agree not to kill him. This was their intent! Remember Hashem, who said that Kofer does not apply here; prevent Go'elei ha'Dam from [such extortion, i.e.] increasing financial destruction.
Malbim: Mention Hashem's name and swear [that Go'el ha'Dam may not kill my son], for this is unlike Go'el ha'Dam of the Torah, who kills a stranger that killed his relative. Here, also the murderer is his brother. 3 Killing him only increases destruction. His ire over his brother will destroy the other brother. Use your royal power to decree that he not kill him!
Makos 9b: The Arei Miklat are spaced evenly (so that they are not too far from any place in Eretz Yisrael), and we must prepare the way with signs showing how to reach them.
How could she tell David to take a Shevu'ah with Hashem's name that was not needed (because her story was not true?! - PF)
What is the source that the law of Go'el ha'Dam does not apply to one who killed a relative? He avenges the murder of an innocent person, and kills one who deserves to die! Why did Malbim not say that it does not apply here because they seek to kill for inheritance, and not due to anger? He makes the story as close to the case of Avshalom as possible. (PF)
Why did David swear that he will not die?
Ralbag #1: He is not Chayav Misah based on Torah law, for there were no witnesses.
Ralbag #2: Even if he was Chayav Misah based on Torah law, the king can exempt for Hora'as Sha'ah.
Kli Yakar citing Mahari: David consented to make a sign for her, like Hashem made for Kayin (refer to 14:11:1:4).
What is the intent of "hair of your son"?
Radak: Hair of his head. Kli Yakar - even though it falls off by itself, they will not make any fall off. All the more so they will not strike him!
