Why did he say "la'Mo'ed ha'Zeh ka'Es Chayah"?
Rashi: Just like today you are alive and b'Shalom, so you will be next year, embracing a son.
Radak: It is a time when it is feasible for you to give birth, after seven or nine months. Chazzl call a Yoledes 'Chayah', e.g. 'a Chayah may wear shoes' [on Yom Kipur - Yuma 73b].
Ralbag, Malbim: The moment I speak is Es Chayah. The past is 'dead' (not in existence), and the future was not 'born' yet. Only the present is 'alive'.
How could he promise her? We do not find that Hashem told him that she will have son!
Radak #1: Perhaps Hashem told him (even though it is not recorded).
Radak #2: He was confident that Hashem would fulfill Elisha's word. It says about a Tzadik "va'Sigzar Omer v'Yakam Lach" (Iyov 22:28). It says about Shmuel ha'Navi "v'Lo Hipil mi'Kol Devarav Artzah" (Shmuel I, 3:19). Pirkei d'R. Eliezer 32 says "Retzon Yere'av Ya'aseh" (Tehilim 145:19) - Hashem did the Navi's desire, and she became pregnant and gave birth.
Before, he did not speak to her in the second person. Why did he now do so ("At")?
Kli Yakar citing Mahari: Now he saw that she properly guards (her distance from him).
Why did she say "Al Adoni"?
Rashi: Do not tell me that I will embrace a son, if later I will bury him! This is why when her son died, she said "I told you, do not mislead me!"
Radak citing Targum Yonasan: Please, my master!
Why did she say "Al" twice?
Radak: This was to strengthen the matter.
Why did she say "Al Techazev"?
Rashi: Do not show to me something that will cease! This is like "Asher Lo Yechazvu Meimav" (Yeshayah 58:11) 1 . You can request mercy and a son will be given to me, but please give to me only a viable 2 son!
Radak citing Targum Yonasan: Do not make your words false.
Kli Yakar citing Pirkei d'R. Eliezer 32: My husband is old, and I ceased to menstruate. I cannot have a son!
QUESTIONS ON RASHI
Rashi writes that she said 'give to me only a viable son.' Why would she think that the baby will be a Nefel (stillborn)?
Malbim: "You will embrace a son" implies that you will merely embrace him, but he will not live long.
Perhaps she already gave birth to such babies, and they died 1 . (PF)
