Seeing as the angels knew where Sarah was, why did they ask Avraham where she was?
Rashi #1: It is good manners to ask one's host about the hostess and one's hostess about the host. 1
Rashi #2 (citing the Gemara in Bava Metzi'a 87a): They wanted to endear Sarah on Avraham, when he would proudly answer that she was in the tent. 2
Seforno: The purpose of the current Sh'lichus was to impart the good news to Sarah that she was about to conceive a son, so that she would rejoice and offer thanks to Hashem - thereby perfecting the conception. 3
Rashbam: They were simply opening a conversation. 4
We learn this from the dots on the 'Alef', the "Yud' and the 'Vav', as Rashi explains. If only Sarah had been there, they would have asked "Ayo" (where is he, your husband - Hadar Zekenim). See also Ba'al ha'Turim.
This explains why they asked where where Sarah was but does not answer the question.
Rashbam: Like we find often by the Shechinah
What is the significance of Avraham's reply "Hinei ba'Ohel"?
Men should not ask at all about women (Kidushin 70b)!
Riva #1: Angels are different.
Riva #2, citing Smag: One may not make her husband a Shali'ach to greet, but one may ask her husband about her.
What is the significance of the dots over the 'Alef', 'Yud' and 'Vav' in the "Eilav"?
Rashi: When there are more letters with dots, we expound them. When there are more letters without dots, we expound them. 1
According to Rashi, the Torah could have put dots just over the Lamed, and we would have expounded the other three letters! Why did it put dots on the other three?
Nimukei Yosef (Bava Metzi'a 52 DH Al Yedei): Had it put dots just over the Lamed, we would expound only "Ayo", that one asks a wife about her husband. Rashi (Bava Metzi'a 87a DH Limdah) says that the dots uproot the word. I.e. since there are dots on three letters, we learn that they did not need to ask about Sarah, for they knew. They asked only because it is Derech Eretz.
Hadar Zekenim #1: It is not normal to begin with dots on just one letter. 1
Hadar Zekenim #2: Also, it might look like the Lamed is deleted.
A Mishnah (Pesachim 9:2) says that there is a dot [only] on the Hei in Rechokah (Bamidbar 9:10)! Maseches Sofrim 6:3 says similarly about u'Veinecha (of Sarah) and uv'Kumah (of Lot)! Perhaps Rashi means that it is improper to begin, i.e. the first word in the Torah with dots should not have only on one letter. (PF)
Temanim write the Nikud above the letters. It seems that also others used to do so. (PF)
Pnei David: Minchah Belulah rejected this answer, for the dots are written in the Sefer Torah, but cantillation or vowels are not, and if they are written in a Sefer Torah they disqualify it (YD 274:7)! He did not see that R. Bechayei says this answer. (I can understand this answer only if the dots are mid'Rabanan. See, however, R. Chaim Paltiel (Shemos 17:9) and Me'iri (Kiryas Sefer 2:1) who maintain that they are a tradition from Sinai. (PF))