Sarah said that Avraham was old (18:12). Why did HaSh-m quote her as having said that she was old?
Rashi: To avoid friction between Avraham and Sarah, 1 since to say that one's husband is old 2 and cannot have children can be hurtful. 3
Ramban, Rashbam, Moshav Zekenim, Da'as Zekenim: "Ani Zakanti" is synonymous with "Acharei Belosi Hayesah Li Ednah," so HaSh-m told the absolute truth. HaSh-m did hold back part of the truth, in that He said "va'Ani Zakanti," and not "va'Ani va'Adoni Zekenim."
We learn from here that one is permitted to lie for the sake of peace.
Da'as Zekenim: I.e. he does not ejaculate.
Moshav Zekenim, Da'as Zekenim, Hadar Zekenim: We can say that HaSh-m totally deviated. Sarah saw a sign of returning to her youth (Dam Nidah), but she could not believe that Avraham would be able to father a child.
Why did HaSh-m take Sarah to task for laughing, but not Avraham, who laughed too (17:17)?
Ramban: Because Avraham's external laughter was one of joy, 1 whereas that of Sarah, who laughed 'in her heart,' was a laugh of mockery. 2
Moshav Zekenim: Sarah publicized the predicted miracle among her neighbors. It was proper not to fulfill it, for HaSh-m prefers doing miracles covertly. She then denied (the predicted miracle), for she feared lest (due to the publicity) it not be fulfilled. Avraham prostrated when he heard, amidst gratitude.
Seeing as Sarah did not know that the guests were angels (as the Ramban explained in the previous Pasuk), why did HaSh-m take her to task?
Ramban: Because she mocked the suggestion that she would have children. She should have believed that it was possible, or have responded with 'Amen!'
Who reprimanded Sarah?
Rashbam: It was the angel speaking in the name of HaSh-m. 1
According to the other commentaries, it was HaSh-m Himself who addressed Avraham.
QUESTIONS ON RASHI
Rashi writes: "'And I have become old' - The verse alters [Sarah's words] for the sake of peace, for she had actually said, 'My husband is old.'" But Sarah did in fact say, "After I have wrinkled, will I yet be rejuvenated?" (18:12). In other words, the verse merely selects which of her words to report; how can this serve as a source that one can alter a person's words for the sake of peace?
Gur Aryeh: Sarah only laughed due to the combination of both reasons - that she had aged, and also that her husband was old. Had there been but one factor, she would not have laughed. HaSh-m told Avraham that she laughed over the factor of her aging alone; and that is our Sages' source that one may alter the truth for the sake of peace (see Bava Metzia 87a).