Why did Eliezer specifically ask for a girl who is a Ba'alas Chesed for Yitzchak?
Rashi: Because the house of Avraham was steeped in Chesed, and she would be the right girl to enter into that household. 1
The commentaries also explain that she would be the ideal partner for Yitzchak, to balance his Midas ha'Din. 2
What is the meaning of "Osah Hochachta"?
Rashi, Targum Unk'lus and Targum Yonasan: It means simply that she will be the one whom You (Hashem) chose for Yitzchak (and another woman, whom You did not choose, will not offer me water - Hadar Zekenim, Ramban and Rashbam).
Seforno #1: She is the one whom You chastised and taught Musar, rendering her fit to marry Yitzchak.
Seforno #2 (on Pasuk 44): She is the one whom Hashem designated (Bashert). 1
As the Gemara says in Sotah (2a) 'Forty days before a baby (boy) is formed, a Heavenly Voice announces "the daughter of P'loni is designated for P'loni" '.
How could Eliezer be so sure that Hashem had already crowned his efforts with success?
Rashi: He wasn't; "u'Bah Eda... " was a prayer 1 for success.
Da'as Zekenim: Ta'anis 4a says that Eliezer asked improperly (perhaps a girl not proper for Yitzchak will do so). According to Rashi, he prayed properly!
Note, according to Rashi, u'Bah Eida" was a Tefilah, whereas according to the Ramban and the Rashbam, it is the first part of the Pasuk that was a Tefilah.
If it was integral to the Shelichus of Eliever for the bride to be from Avraham's family (as Rashi points out), why did Eliezer omit it from his Tefilah?
Eliezer asked that she will say "drink, and I will also give to your camels to drink." She offered to give to the camels only later!
Mishnas R. Aharon 1 p.138: She did better than he thought, that she will discuss giving to him and his camels in the same utterance, thereby equating them. Also, Tzadikim say little and do much. Also, it is hard for a man to receive so much Chesed (she feared to offer so much at once).
Why did Eliezer ask only for a sign of Chesed, but not of Yir'as Shamayim? Perhaps she serves idolatry,like her father and brother!
Lev Eliyahu (Bereishis p.69): One who has good Midos is prepared for the highest levels. Corrupt Midos is a bad illness; few are cured from it.
How could Eliezer rely on Nichush (omens - Chulin 95b)? Some forbid even for Bnei Noach (Sanhedrin 56b)!
Moshav Zekenim, Riva citing R. Tam and Rashbam: He did not rely on it. He immediately took out the ring and bracelets, but gave them to her only after asking who her father is. "Al Yadeha" means due to her; she caused him to say a Brachah, which is worth 10 gold pieces (Chulin 87a). 1
A slave does not own anything! (Perhaps Avraham authorized him to give gifts.) This does not explain giving the ring. (PF)
רש"י: אותה הכחת- ראויה היא לו וכו': למה לא היה בזה איסור של ניחוש?
גור אריה: גם אלמלא הניחוש היא ראויה ליצחק מפני שהיא גומלת חסדים, וניחוש אסור כאשר עושה דבר מחמת ניחוש מבלי שיש בזה טעם.
גור אריה: לדבר מצוה מותר.
רש"י: אותה הכחת- ראויה היא לו וכו': בגמ' (חולין דף צה:) כתוב שניחוש שאינו כניחוש של אליעזר אינו ניחוש, והרי אצל אליעזר לא היה איסור ניחוש?
גור אריה: כוונת הגמ' שאם המנחש אינו סומך על הניחוש כמו שסמך אליעזר, אין בזה איסור ניחוש.
רש"י: ובה אדע- לשון תחינה: מנין לפרש כך?
גור אריה: אין לפרש שאמר כך בוודאות כי מנין לו לדעת שהיא ממשפחת אברהם? אלא הוא אמר זאת בדרך תחינה.