What is it that Hashem remembered about Rachel?
Rashi: Hashem remembered two things - (a) How she handed over the Simanim to her sister; 1 and (b) How distressed she was over the fear lest Yaakov divorce her due to barrenness, and Esav would marry her, 2 as a result of which He now answered her prayers. 3
In this verse, Hashem remembers Rachel, and grants her pregnancy. Wouldn't it be more appropriate that the verse use Shem Havayah, which indicates the Attribute of Mercy, rather than Elokim, which indicates the Attribute of Justice?
Birth is an example of Hashem's Gevurah, as He brings out the child from potential to actual. We refer to birth in the second Berachah of the Amidah (Gevuros). Also refer to 18:10:2.3:2, and the notes there.
The Gemara (Ta'anis 2a) teaches that Hashem does not give over the key of birth to any messenger. Maharal (Gevuros Hashem Ch. 52, p. 226) - Absolute emergence from the potential to the actual is only from Hashem. [Angels are entrusted with the regular course of the world, not with creation itself.] That is why the key to childbirth is never entrusted to them. See Maharal (Tif'eres Yisrael Ch. 27, p. 81) - Midas ha'Din brings an increase in children; emerging from the potential to actual, comes through Din. Maharal (Gevuros Hashem Ch. 71, p. 326) - To bring about a change one must exert force, which is Din (EK).
Why does it say "va'Yizkor" and "va'Yishma"?
Ohr ha'Chayim: Hashem remembers His pious ones even before they pray.
Ha'amek Davar: She had great deeds; Tefilah does much (the deeds did not suffice by themselves).
QUESTIONS ON RASHI
Rashi writes: "'Hashem remembered Rachel' - He remembered to her [merit] that she had given over her signs to her sister, and that she was afraid of ending up with Esav...." Why doesn't Rashi explain simply, that Hashem remembered Rachel herself?
Gur Aryeh: Remembering applies to something that is not always present (i.e. an event in the past). The righteous Rachel was always in the forefront before Hashem; as the verse says, "The eye of Hashem is upon those who fear Him" (Tehilim 33:18).
Rashi writes: "Hashem remembered.... that she had given over her signs to her sister." Why specifically this merit, and not the many other Mitzvos that Rachel had done?
Gur Aryeh: Seeing as Rachel had given up so much, so that her sister should not leave her marriage in shame, it could not be that Rachel would have to leave her own marriage in shame! 1 (Rashi - She feared lest Yaakov divorce her due to her inability to bear children.)
This is an example of Midah-k'Neged Midah; or as Chazal express it, "In the very thing that the Tzadik took pains over, would his descendants falter?!" (Yevamos 121b).
Rashi writes: "As the Paytan wrote, 'ha'Admon, k'Vat she'Lo Chalah...' (Kerovos for Rosh Hashanah, Shacharis Day 1, beg. 'Even Chug')." What does the word 'Chalah' mean in this context?
Gur Aryeh: Although in other contexts 'Chalah' means illness, or the travail that accompanies birth, in this context it means birth itself. 1 The stanza of the Piyut means, 'The red one (Esav) - when he saw that she (Rachel) had not given birth / he desired to take her for himself, and she became panicked.'