Why does the Torah juxtapose the names of Milkah's children to the Akeidah?
Rashi and Seforno: After the Akeidah, Avraham thought to himself what would have happened with Hashem's promise of children had Yitzchak been sacrificed. He therefore considered marrying him to one of the children of Aner, Eshkol and Mamrei. 1 That was when Hakadosh-Baruch-Hu informed him of the birth of Rivka - Yitzchak's Bashert.
Targum Yonasan: Because Avraham was informed of the birth of Rivka after the Satan told Sarah that Avraham had Shechted Yitzchak (even though he had only been bound) as a result of which she died of heartbreak. 2
Assuming Hashem told him the news immediately after the Akeidah, why does the Torah write "Acharei" (which generally means a long time afterwards) and not 'Achar', which means immediately.
Chizkuni: It seems that 'Achar' means immediately (exclusively), whereas 'Acharei' can mean long afterwards too (but not exclusively).
Perhaps this a support for the commentaries who disagree with Rashi, who hold that Rivka was already eleven years old at the time of the Akeidah, and that she married Yitzchak when she was fourteen,
Why did Hashem see fit to tell Avraham all this?
Rashi (Pasuk 23) and Ramban (Ibid.): The purpose of this Parshah is the statement that Besu'el bore Rivka; all the rest is secondary.
Ramban: Because Milkah was the daughter of Avraham's brother Haran, and Hashem saw fit to inform him that his older brother (Nachor) 1 had been blessed with all these children from the daughter of their deceased brother. 2
Why does the Torah write "Milkah Gam Hi"? What is the close comparison between Sarah and her sister Milkah?
Rashi: The Pasuk is actually comparing the families of Avraham and (his brother-in-law) Besu'el, inasmuch as the latter, like the former would eventually do, comprised twelve tribes - eight from his main wife, and four from his concubine.
Ramban and Targum Yonasan: When Hashem performed a miracle enabling Sarah to bear children in her old age, He did the same on behalf of Milkah, who also gave birth in her old age. 1
Seforno: "Gam Hi" means that besides the concubine (Re'umah), Milkah too, bore children to Nachor. 2
Because, had she given birth to them in her younger years, Avraham would have been bound to know about it.
It is strange to say this however, since a. It has not yet mentioned Re'umah and b. It would be more appropriate to say that also Re'umah bore children ... (indeed, the Torah writes "Gam" there as well, and writing it in both places is truly odd).