Why did Avraham make Eliezer swear that he would follow his instructions?
Seforno #1: Refer to 24:1:1:2.
Seforno #2: Refer to 24:1:2:2.
Ohr ha'Chayim (1): Because Eliezer harbored thoughts that Yitzchak should marry his own daughter; the Shevu'ah would serve to dispel them. 1
Malbim (2): He was concerned lest Yitzchak follow Eliezer's counsel, for he 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'Hyeh Brachah" (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 (on Pasuk 1): Because there was nobody in Kena'an who was worthy of marrying Yitzchak.
Lev Eliyahu (Bereishis p.70): Kena'anim have corrupt Midos. They come from Cham, who corrupted in front of his father and was permanently cursed. Otherwise, he would have taken Eliezer's daughter!
What is he 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, Hashem would punish him in this world and in the next.
Ha'Emek Davar: Avraham normally spoke this way, to accustom people to say that Hashem oversees Heaven and earth.
Why did Avraham mention here that Hashem was also "G-d of the earth", but omit it later in Pasuk 7?
Rashi (in Pasuk 7): Because whereas now, thanks to Avraham's efforts, Hashem was also the G-d of the earth (i.e. 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: Hashem is called G-d of Eretz Yisrael (but not of Chutz la'Aretz). 2 This Pasuk is referring to Eretz Yisrael, and Pasuk 7 refers to when Avraham lived in Charan or in Ur Kasdim.
Seforno: Here Avraham alludes to 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.
Why did Avraham issue this command to Eliezer and not to Yitzchak directly?
Ramban #1: He intended to send him on this mission to Charan in any event (either whilst 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: 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, R. Chaim Palti'el: At the time, Yitzchak was in Be'er Lechai Ro'i 3 (Pasuk 62 says that he came from there), and Avraham feared lest he himself die before Yitzchak returns.
Avraham did not want Yitzchak to go himself, for he did not want him to leave Eretz Yisrael, as it connotes in Pasuk 6 (R. Bechayei, Pasuk 6).
Which explains why Avraham inserted "who controlled all that he owned".
Moshav Zekenim: Avraham had sent Yitzchak there, for Aner, Eshkol and Mamrei were asking to marry their daughters to Yitzchak, and Avraham did not want to explicitly refuse them. Now, when Yitzchak returned, Yitzchak could say "I already engaged a girl from my family." (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 Bekirbo"?
Sifsei Chachamim (on Pasuk 8): To include the daughters of Aner, Eshkol and Mamrei in the prohibition.
Oznayim la'Torah #1: Because Hashem promised Avraham that his children would eventually conquer Eretz Kena'an and exterminate its inhabitants, something that would have been nigh-on impossible to achieve had they descended from them. 1
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
Oznayim la'Torah: A good reason as to why Eliezer should not take a wife for Eliezer from the 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 were 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 Hashem sent him to Kena'ani, 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 Yakov 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,
Why did Avraham say "Ashbi'acha", and Yakov said [to Yosef] "Hishava Li"?
Ha'Emek Davar: A master can make his slave swear Bal Korcho (against his will). 1
Ha'Emek Davar: Likewise, a king can force someone to swear (like Shlomo forced Shim'i), and the Sanhedrin forced the Kohen Gadol to swear. It seems that he need not answer Amen.
Why did Avraham mention Hashem in the Shevu'ah, and Sha'ul asked David to swear ba'Shem (Shmuel 1:24:21), but Yakov did not, when he asked Yosef to swear?
Ha'Emek Davar: Sha'ul was concerned lest David annul the Shevu'ah in his heart. He asked him to say Hashem's name; surely he would not annul the Shevu'ah, which would make his mention of Hashem's name l'Vatalah! If someone imposes a Shevu'ah on others, he must explicitly say Hashem's name.
Perhaps Yakov 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 Hashem'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'Emek Davar: Surely the Torah did not record earlier words in which Avraham told Eliezer to try to find a wife for Yitzchak.