Why did Avraham make Eliezer swear that he would follow his instructions?
Seforno #1: Refer to 24:1:1:2.
Seforno #2: Refer to 24:1:3:2.
Ohr ha'Chayim (to 24:1): Because Eliezer harbored thoughts that Yitzchak should marry his own daughter; the Shevu'ah would serve to dispel them. 1
Malbim (to 24:2): He was concerned lest Yitzchak follow Eliezer's counsel, since Eliezer was "Zekan Beiso, ha'Moshel b'Chol Asher Lo".
Ohr ha'Chayim: It would not suffice to tell him 'you are from Kena'an, who was cursed; you cannot cling to my seed, which was blessed,' lest Eliezer think that he ceased to be cursed, for "ve'Heyeh Berachah" (12:2) applies to all Avraham's household, and "v'Nivrechu Vecha" (12:3) applies to those around him. Avraham forbade a wife from those around him to refute this notion!
Why did Avraham need to look for a wife for Yitzchak in Charan? Why could he not find someone in Eretz Kena'an?
Ramban: Refer to 24:1:2:4**
Seforno: Refer to 24:1:2:4*.
Lev Eliyahu (Bereishis, p. 70): Kena'anim have corrupt Midos. They descended from Cham, who behaved in a corrupt manner in front of his father and was permanently cursed. Otherwise, he would have taken Eliezer's daughter!
What is the significance of, "The G-d of the Heaven and the G-d of the earth" by which Avraham made Eliezer swear?
Seforno: He was warning him that, in the event that he would break that oath, HaSh-m would punish him in this world and in the next.
Ha'amek Davar: Avraham normally spoke this way, to accustom people to say that HaSh-m oversees Heaven and earth.
Why did Avraham mention here that HaSh-m was also "G-d of the earth," but omit it later in verse 24:7?
Rashi (in 24:7): Because whereas now, thanks to Avraham's efforts, Hashem was also the G-d of the earth (the people on earth acknowledged Him), when Hashem took him from his father's house (which is the period to which Avraham referred in Pasuk 7), He was only G-d of the Heaven, but not yet of the earth. 1
Ramban: Whereas the current Pasuk is referring to Eretz Yisrael, Pasuk 7 is referring to when Avraham lived in Charan or in Ur Kasdim ? and Hashem is called G-d of Eretz Yisrael (but not of Chutz la'Aretz). 2
Seforno: Because here Avraham is referring to the punishment for breaking that oath - Refer to 24:3:3:1, whereas in Pasuk 7, he was praying to the G-d of the Heaven to send an angel to accompany Eliezer.
Riva: This is why we do not say "Melech ha'Olam" in Birkas Avos, because when Hashem began to be the G-d of Avraham, he was not yet (known as) ?Melech ha'Olam?.
As the Ramban will explain (see Ramban to Vayikra 18:25). See also Kesuvos 110b.
Why did Avraham issue this command to Eliezer and not to Yitzchak directly?
Ramban #1: Because he intended to send him on this mission to Charan in any event (either while he was still alive or after his death). 1 Consequently, knowing that Yitzchak would never go against his wishes, to contravene the oath that Eliezer had made, there was no point in making him swear as well.
Ramban #2: Because he was ordering Eliezer, in his (Eliezer's) capacity as manager of his estate, to marry off Yitzchak, and to see to it that he inherits all his property to that effect. 2
Moshav Zekenim and R. Chaim Palti'el: Because at the time, Yitzchak was in Be'er Lachai Ro'i 3 - See Pasuk 62, and Avraham was afraid that he may die before Yitzchak returns.
Avraham did not want Yitzchak to go himself because he did not want him to leave Eretz Yisrael, as it implies in Pasuk 6 (R. Bachye).
Which explains why Avraham inserted "ha?Moshel be?Chol Asher Lo".
Moshav Zekenim: Avraham had sent Yitzchak there, since Aner, Eshkol and Mamrei were asking to marry their daughters to Yitzchak, and Avraham did not want to explicitly refuse them. But when Yitzchak returned, he could say that he was already engaged to a girl from his own family. (and even though one may not deceive even Nochrim, it is permitted for Darchei Shalom, to avoid offending them - PF.)
Why did Avraham add, "Asher Anochi Yoshev b'Kirbo"?
Sifsei Chachamim and Gur Aryeh (both to 24:8): To include the daughters of Aner, Eshkol and Mamrei in the prohibition. 1
Oznayim la'Torah #1: Because HaSh-m promised Avraham that his children would eventually conquer Eretz Kena'an and exterminate its inhabitants, something that would have been nearly impossible to achieve had they descended from them. 2
Oznayim la'Torah #2: Seeing as there was no woman in the world worthy of marrying Yitzchak, it would have entailed converting a woman and teaching her the basics of Judaism. But that would only have been possible if she was away from her family and friends - free from their sphere of influence, not if she was a native of Kena'an.
Ha'amek Davar #1: Avraham suspected that Eliezer did not want to toil to go to Avraham's family and that he would take a nearby girl and claim that she is from Aram.
Ha'amek Davar #2: These words include a girl from another nation living in Eretz Yisrael over whom the Kena'anim rule who were considered like Kena'anim.
Why did Avraham prefer a girl from his family, who were idolaters, over people close to him, who followed his teachings?
Moshav Zekenim: Avraham's family was truthful. He knew that if he would draw them close, they would learn Yir'as Shamayim from him. 1
Malbim: The Kena'anim were cursed. They had corrupt Midos. Avraham sensed that this is why HaSh-m sent him to Kena'an, to fix them! Bad Midos are passed on to children, but false beliefs (e.g. idolatry) are not.
Avraham was with his family until the age of 75, and they did not learn Yir'as Shamayim from him, nor did Lavan in 20 years that Yaakov was with him! Perhaps there, the idolaters were the hosts, and older, and the entire city were idolaters, so they were not open to learning from them. Here, he seeks a younger girl, who will live among Tzadikim, who will supply her needs, and a woman normally looks up to her husband.
According to the opinion that the Shevatim married Kena'ani women (see Rashi to 37:35), how did they violate Avraham's command?
Gur Aryeh (to 38:2): Once twelve tribes were born, they were considered to be a nation. A woman marrying in would be subsumed into the nation of Yisrael.
Why did Avraham say "Ashbi'acha," whereas Yaakov said [to Yosef] "Hishava Li" (47:31)?
Ha'amek Davar: A master can make his slave swear Bal Korcho (against his will). 1
Ha'amek Davar: Likewise, a king can force someone to swear (like Shlomo forced Shim'i- Melachim I 2:42), and the Sanhedrin forced the Kohen Gadol to swear (Yoma 18b). It seems that he need not answer Amen.
Why did Avraham mention HaSh-m in the Shevu'ah; and Shaul likewise asked David to swear Ba'Sh-m (Shmuel I 24:21), but Yaakov did not do so when he asked Yosef to swear (47: 29-31)?
Ha'amek Davar: Shaul was concerned lest David annul the Shevu'ah in his heart. He asked him to say HaSh-m's name; surely he would not annul the Shevu'ah, which would make his mention of HaSh-m's name l'Vatalah! If someone imposes a Shevu'ah on others, he must explicitly say HaSh-m's name.
Perhaps Yaakov saw no need to impose a severe Shevu'ah on Yosef (PF). The Ra'avad holds that there are no lashes for violating a Shevu'ah without HaSh-m's name (Ran Nedarim 2a Sof DH u'Shevu'os).
Why do Avraham's words imply that Eliezer has control over whom Yitzchak will marry?
Ha'amek Davar: Surely there were earlier words in which Avraham told Eliezer to try to find a wife for Yitzchak, which the Torah did not record.