What did Eliezer mean when he asked Lavan and Besu'el to do "Chesed ve'Emes" with his master?
Seforno: By "Chesed" he meant that they would negate their own wish to marry Rivkah off to someone from their own country, and by "Emes,' to do what was for the best advantage for their daughter - by marrying her off to the house of Avraham.
Ibn Ezra: When one undertakes to do something - that is Chesed. When one carries out one's word - that is Emes. 1
Malbim: Emes is HaSh-m's decree. Chesed is that they will not negate it through their free choice, through demanding that Yitzchak come to see her first, and refusing to send her with Eliezer.
Ha'amek Davar: It is Chesed of Emes, for it is clear that this is the Emes (correct thing to do).
Which is what "Chesed ve'Emes" always means.
What did Eliezer mean when he said that he would "turn to the right or to the left"?
Malbim: He meant that he would take a daughter from Yishmael or from Cana'an.
Ha'amek Davar: I will seek counsel.
How could Avraham possibly have said such a thing, bearing in mind a. his rejection of Lot - See 13:9, and the Midrash, which declared Lot unfit to mix with the family of Avraham, and b. Sarah's statement that Yishmael was unworthy of inheriting together with Yitzchak - See 21:10. See Oznayim la'Torah.
The Rashbam seems to concur with his explanation.
QUESTIONS ON RASHI
Rashi writes: "'To the right'- to the daughters of Yishmael... 'To the left' - to the daughters of Lot." What is the deeper meaning behind this?
Gur Aryeh: Yishmael is to the right, and Lot is to the left, for reasons that are known. 1
We may explain that Yishmael is the Kelipah, (the "shell" or excess) in the trait of Chesed, which is associated with the right-hand side (this explains why they are promiscuous in immorality). Lot is the Kelipah in the trait of Din, associated with the left-hand side. (EK) Also refer to 21:12:2.1:1 and the note there.
Rashi writes: "... The daughters of Yishmael... of Lot." But when Avraham initially commanded Eliezer ? in Pasuk 8 - Rashi explained that he told him [in such an event] to take from the daughters of Aner, Eshkol and Mamrei (Rashi to 24:8)! Why did Eliezer change this?
Malbim (to 24:37): He was supporting his (false) claim that Avraham preferred a girl from his family.
Gur Aryeh (to 24:8): Avraham gave two directives to Eliezer - a) go to 'my land,' b) to 'my birth' (i.e. my family) (24:4). 1 Eliezer first went to Nachor's family in the town of Charan, where he could fulfill both conditions. If that were to fail, he would turn to Lot or Yishmael, Avraham's family, so that at least one condition would be fulfilled. Only if none of the family would agree at all was Eliezer to take from Aner, Eshkol and Mamrei.
Refer to 24:4:1.1:3.