What are the connotations of "... ad Midrach Kaf Ragel"?
Rashi #1: It means that even passing through their land without permission is prohibited.
Rashi #2 (citing a Midrash): It means that Yisrael will not receive any of Edom's land until the day that Hashem's Foot will tread on Har ha'Zeisim. 1
Rosh (in Pasuk 3, citing R. Shmuel bar Nachmani): It means that Yisrael will not receive any of Edom's land until the one about whom it says "Darach Kochav mi'Ya'akov" - Mashi'ach - arrives, and then "ve'Alu Moshi'im ? Lishpot es Har Eisav." 2
Oznayim la'Torah: Because Eisav opted to live in Har Se'ir, leaving Cana'an to Yisrael, and the Halachah is like Shmuel, who holds that brothers do not have right of way through each other's property. 3
Rashi: As the Pasuk states in Zecharyah, 14:4. See also Ba'al ha'Turim.
As opposed to Rav, who maintains that they do. See Oznayim la'Torah.
From whom did Eisav inherit Har Se'ir?
Rashi: From Avraham, to whom Hashem gave ten nations, seven to Yisrael and three - the Keini, Kenizi and Kadmoni - to Eisav and to Amon and Mo'av, the sons of Lot, respectively.
On what merit did Eisav receive Har Se'ir as an inheritance?
Rashi (in Divrei Hayamim 1, 1:1): Out of love for Yitzchak ? in fulfillment of the promise that He made to him to increase bis children and give him rulership over all.
Targum Yonasan: As a reward for honoring his father. 1
See Ba'al ha'Turim.
On what merit did the sons of Lot receive an inheritance from Avraham?
Rashi: As a reward for accompanying Avraham down to Egypt and for remaining silent when they said that Sarah (his sister) was Avraham's sister, for which Hashem gave him the status of his (Avraham's) son.
Targum Yonasan: Refer to 2:19:2:2.
Why did Hashem need to explain to Yisrael why they were not permitted to fight Edom, Mo'av (in Pasuk 9-12) and Amon (in Pesukim 19-23)?
Rashbam #1: To preempt the question the people would ask in fear - why, seeing as they were about to embark upon the conquest of Cana'an, Hashem had ordered them to pass by these three lands and not conquer them.
Rashbam #2: To encourage the people, inasmuch as, when they will see how Hashem granted these nations their inheritance in honor of their (Yisrael's) forefathers, then they can be rest-assured that He will certainly grant them the inheritance that He swore to their forefathers that He would give to them.
Bava Kama 38a (regarding Mo'av): To disillusion Moshe, who thought that, since Hashem had ordered them to take revenge against Midyan, how much more so would He order thm to take revenge against Mo'av! 1
Da'as Zekenim, Hadar Zekenim and Rosh (all in Pasuk 9): To counter the mistaken belief that they belonged to Yisrael - since Yisrael were promised the lands of the Chivi and the Refa'im, 2 and Se'ir is often called 'Chivi', 3 and Amon and Mo'av, 'Eretz Refa'im'.
Refer to Bamidbar 22:3:151:1 & 2 and note.
Da'as Zekenim, Hadar Zekenim and Rosh: Because they trusted in their wisdom and strength, they rebelled against Hashem, and Hashem gave them over to weaker nations
Because they smelled the ground like a snake (Chivya) In order to know what to plant. .