What is the significance of the fact that Rivkah appeared on the scene before Eliezer had finished Davening?
Seforno (to 24:45): It is a sign that HaSh-m agrees wholeheartedly with the request.
This is a classical case of Hashem answering a sincere Tefilah before it has been asked - as the Navi writes in Yeshayah 65:24 ?Terem Yikra?u va?Ani E?eneh?. 1
Why does the Torah see fit to mention that Besu'el, Rivkah's father, was the son of Milkah?
Ramban, Hadar Zekenim (in 24:24), Seforno, and Ohr ha'Chayim (to 24:24): 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 the side of his father (Avraham's brother) and the side of 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 24:45, 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)