What are the connotations of "ve'Lo Yidbak be'Yadcha Me'umah min ha'Cherem"?
Makos, 22a: It is a La'av against deriving benefit from Avodah Zarah. Consequently, someone who plows with a plow made of Asheirah-wood or who cooks with Asheirah-wood is subject to Malkos. 1
Avodah Zarah, 34b: "Me'umah" implies that anything to do with Avodah Zarah is Asur be'Hana'ah, and that consequently, if someone betroths a woman with the dung of calves of Avodah Zarah, the Kidushin is not valid. 2
Avodah Zarah, 48b: "Min ha'Cherem" implies that the wood of an Asheirah only renders Asur on its own, but not if it is combined with Heter. Consequently, if one plants vegetables underneath an Asheirah-tree, the vegetables are permitted - since the shade caused them to grow together with the earth. 3
Yerushalmi Avodah Zarah, 5:12: "Me'umah" teaches us that if even the smallest mount of Avodah Zarah falls into a pot of food, it is not subject to Bitul and renders the entire pot Asur. 4
What is "Lema'an Yashuv Hashem me'Charon Apo " referring to?
Rashi: It is referring to "Hakeh Sakeh" - in Pasuk 16 - 'When you smite the inhabitants of the Ir ha'Nidachas, Hashem's anger will abate.
Why does the Torah mention "Charon Apo" here?
Rashi: Because as long as there is Avodah-Zarah in the world, there is burning anger in the world.
Avodah Zarah, 34b: Because as long as the Resha'im 1 exist in the world, there is burning anger in the world.
Who steals from the spoil of the town and transgress "ve'Lo Yidbak ... ". See Torah Temimah, note 61.
Why does the Torah insert the word "Vehirbecha"?
Oznayim la'Torah: In case we are worried at the loss of an entire town, the Torah reassures us that Hashem will restore the loss by causing us to proliferate. 1
See Ba'al ha'Urim.
Why does the Torah insert the (otherwise superfluous) phrase "Venasan l'cha Rachamim ... "?
Da'as Zekenim. Hadar Zekenim (on Pasuk 7) and Rosh (on Pasuk 17): Since you did not have mercy on those who anger Hashem, He will have mercy on you.
Or ha'Chayim: Performing a cruel act (killing the entire city) causes a person to become cruel. Hashem is therefore promising to counter this by instilling the Midah of compassion into all those who carried out the Din against the residents of the Ir ha'Nidachas..
Tosefta Sanhedrin, 14:1 #1 (according to R. Akiva): To teach us to have compassion on the children of Ir ha'Nidachas [and not kill them].
Tosefta Sanhedrin 14:1 #2 (according to R. Eliezer): To teach us to go ahead and kill the inhabitants of the Ir ha'Nidachas and not to worry about the relatives taking revenge, because Hashem will have mercy on you and cause them to love you 1 - inasmuch as they will accept the judgement as Divine retribution. 2
Shabbos, 151a: The double Lashon "Ve'nasan L'cha Rachamim ve'Richamcha" teaches us that Hashem repays someone who has compassion on others and has compasion on him, and vice-versa.
Beitzah, 32b: The double Lashon "Venasan l'cha Rachamim ve'Richamcha" teaches us that someone who has compassion on others is from the children of Avraham Avinu - who was compassionate 3 but someone who does not have compassion is not. 4
Yevamos, 79a: Yisrael have three Simanim (Midos) - 'Rachmanim, Bayshanim and Gomlei Chasadim'; and we learn Rachmanim from this Pasuk.
