What is the meaning of "Nafsheinu Tachteichem Lamus"?
Radak: We will give up our lives (if needed) in place of you to die, if someone wants to kill you.
Malbim: We must give up our lives (if needed) to save you.
Why did they say "Tagidu" (plural)?
Radak #1: She and her father's house may not tell. Surely someone from her father's house was there; she was not alone!
Radak #2: They said also about her father's house, even if her father's house was not there, just like they said "Nafsheinu Tachteichem Lamus" [even about family members not there at the time].
What are "Chesed" and "Emes" that they will do for her?
Radak (12): Chesed is keeping alive her family, who did not help the spies. Emes is keeping her alive.
Malbim: Emes is keeping [all of you] alive, since you did not tell the king about us. Chesed is great gifts and honor that we will give to you when Hashem gives the land to us.
How could the spies swear to nullify a Torah Mitzvah "Lo Sechayeh Kol Neshamah" (Devarim 20:12)?
Tosfos (Megilah 14b): She was from a different nation, and came [with her family] to live in Eretz Kena'an. 1
Rosh Yosef (Megilah 14b): The Yerushalmi (Shevi'is 6:1) says that Yehoshua sent three letters [allowing the Kena'anim to make peace, before Yisrael came to fight]. This applied even to individuals.
Sefas Emes (Megilah 14b): We must say that they swore based on Ru'ach ha'Kodesh.
Pesach Einayim (14b): The Sifri (Beha'aloscha) says that she was from a nation to which "Lo Sechayeh Kol Neshamah" applies!