What does "Aval" mean?
Rashi:" It is true (unbelievable as it may sound)! Sarah will indeed bear you a son!"
Ramban: Although I will bless your son Yishmael, 1 as you requested, however the covenant that I am making with you is with the son that Sarah will bear you.
As the following Pasuk (17:20) goes on to say.
What is the deeper reason for the name "Yitzchak"?
Rashi: The letters of "Yitzchak" represent the ten trials of Avraham ('Yud'), the ninety years of Sarah ('Tzadei'), the eight days of B'ris Milah ('Ches') and the hundred years of Avraham ('Kuf').
What was Hashem teaching us when He added, "and I shall establish My covenant with him (Yitzchak)"?
Rashi #1: Hashem was telling Avraham that He would establish the covenant of Milah with Yitzchak, and not with B'nei Yishmael or the B'nei Keturah. 1
Rashi #2 (in Shabbos, 137b) Before Yitzchak was born, Hashem already established a B'ris with him. 2
Why did Avraham not immediately inform Sarah that she would bear a son?
Ramban #1 (to 18:15): Because he relied on the fact that Hashem would inform her personally the next day. 1
Ramban #2 (ibid.): Because he simply did not have the time. First, he was busy with the Mitzvah of B'ris Milah, then weak from the ordeal; then he was sitting outside when along came the visitors.
Bearing in mind that Sarah too was a prophetess.
QUESTIONS ON RASHI
Rashi writes: "Alternatively, [the letters of Yitzchak's name] allude to the ten (Yud) tests of Avraham..." Why are the ten tests of Avraham relevant for inclusion in the name of Yitzchak?
Gur Aryeh: The main letters of Yitzchak's name are the 100 years (Kuf) and 90 years (Tzadi) of Avraham and Sarah, respectively. Why were they granted a child only then? So that they would have the Mitzvah to circumcise him on the eighth day (Ches). And why was Avraham not commanded in this Mitzvah sooner? Avraham was to be tested ten times (Yud), and one of tests was to undergo Milah specifically in his old age.
Rashi writes: "Yitzchak - due to the laughter (Tzechok); while some say due to the ten tests of Avraham, etc." Why are both explanations necessary?
Gur Aryeh: If only for the first reason, he could have been called "Tzechok." Nor is the second, symbolic reason the main one, for when Yitzchak is born, Sarah also proclaims, "Hashem has made laughter (Tzechok) for me" (21:6).
Rashi writes: "My covenant - i.e. the Bris Milah, will be given [specifically] to the descendants of Yitzchak." How do we know that this [exclusion of all others from the covenant] refers to the Bris Milah, and not merely to the covenant of love between Avraham and Hashem (referred to in Rashi to 17:2)?
Gur Aryeh: The next two verses (17: 20-21) state, "I have heard you regarding Yishma'el... but [nevertheless], I shall establish My covenant with Yitzchak." Those two verses refer to the covenant of love 1 between Hashem and Yitzchak, so this verse must refer to the covenant of Bris Milah.
For Yishma'el is certainly not part of the covenant of Milah, and it would even be unnecessary to emphasize that he is excluded