What is the significance of the fact that Rivkah appeared on the scene before Eliezer had finished praying?
Seforno (Pasuk 45): It is a sign that Hashem agrees wholeheartedly with the request.
Why does the Torah see fit to mention that Besuel, Rivkah's father, was the son of Milkah?
Hadar Zekenim (Pasuk 24), Ramban, Seforno, Ohr ha'Chayim (24), Malbim (24): To tell us that he was the son of Nachor's main wife and not of his concubine, Re'umah. 1
Malbim: It teaches that he was from Yitzchak's family both from his father (Avraham's brother) and his mother (Sarah's sister).
Oznayim la'Torah: This is why the Torah, here and in a number of other places, adds "Eishes Nachor".
Why does it say "Hinei"?
Malbim: This always denotes a Chidush. Besu'el was rich. He never sent Rivkah, rather, slaves. This was the first [and only] time she went.
Why does it say "Rivkah Yotzeis"?
Ohr ha'Chayim: She came out at this moment as a result of Eliezer's prayer.
Malbim: She left her house. 1
Also in verse 45, Eliezer says that [he saw that] she left just before he finished his prayer. He was outside the city. If the city did not have a wall, it is not astounding if he noticed her leaving her house. Why did he not say that she left the city just then, which is reasonable even if it had a wall? (PF)