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.
Or ha'Chayim: Because Eliezer harbored thoughts that Yitzchak should marry his own daughter; The Shevu'ah would serve to dispel them. 1
See Or ha'Chayim.
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. If not, 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.
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: By the same token, bearing in mind that Hashem is only G-d of Eretz Yisrael (but not of Chutz la'Aretz), 2 whereas this Pasuk is referring to Eretz Yisrael, Pasuk 7 refers to when Avraham lived in Charan or in Ur Kasdim.
Seforno: Refer to 24:3:3:1, whereas in Pasuk 7, Avraham 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 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.)
למה הוסיף אברהם "אשר אנכי יושב בקרבו"?
גור אריה (לקמ' פסוק ח): יתור זה בא לרבות שלא יקח מבנות ענר אשכול וממרא. 1
ועיי"ש שפשוט שבנותיהם גם בכלל השבועה, אבל מכאן למד רש"י (לקמ' פסוק ח) שאם משפחת אברהם לא תתן את בתם, יפנה אליעזר לבנות ענר אשכול וממרא.
לסוברים שהשבטים נשאו כנעניות קשה כיצד הם עברו על ציווי אברהם?
גור אריה (לקמן לח,ב): כיוון שכבר נולדו י"ב שבטים והם נחשבים לאומה, הכנעניות בטילות אצלם והן בכלל ישראל.