Why does the Torah write "va'Yikra l'Moshe" (as opposed to 'va'Yikra El Moshe' [See Sifsei Chachamim])?
Rashi (and Ramban, see 12:31:1:3): To teach us that Pharaoh went from door to door crying out, 'Where does Moshe live?' 'Where does Aharon live?'
Targum Yonasan: Although Moshe and Aharon lived in Goshen (in the middle of the country), and Pharaoh's palace was on the border, 1 when Pharaoh called out to them with a sad voice, pleading with him to leave unconditionally, they heard his pleas. 2
Ramban: Moshe and Aharon spent that night (eating the Korban Pesach) in the land of Egypt (not in Goshen), to enable Pharaoh to come to them begging 3 (in fulfillment of the Pasuk earlier, "v'Yardu Chol Avadecha Eileh Eilai, v'Hishtachavu Li Leimor" (11:8)). 4 The moment that Pharaoh issued his request, they sent messengers 5 to Goshen to inform the people that they had permission to leave. 6
Targum Yonasan: And Egypt was 400 Parsah by 400 Parsah!
Ramban (citing Mechilta): But they refused to comply, since 'they were not thieves (i.e. who need to escape secretly),' and Hashem had therefore ordered them to leave in broad daylight, in full view of their erstwhile tormentors (refer also to 12:41:1:3). Moreover, they were under strict orders not to leave their houses until the morning. Refer also to 12:33:2:2.
And because this took place at nighttime, the Torah in Parshas Re'eh (Devarim 16:1) refers to the Redemption as having occurred at night time. See Ramban here, and Rashi to Devarim ibid).
The Ramban did not say who these messengers were. Bnei Yisrael were commanded to stay indoors! Perhaps they were Egyptians, who were eager to help Yisrael leave as soon as possible.
Hadar Zekenim: Pharaoh shouted, 'You are all free;' and Hashem made Pharaoh's voice audible throughout Egypt.
Having stated in 12:30 that Pharaoh rose in the middle of the night, why does this Pasuk repeat the word "Laylah"?
Oznayim la'Torah: To hint at Moshe's response - that they could not yet leave Egypt, seeing as they were under orders not to leave their houses all night. 1
Perhaps it hints at Chazal, who say that the Ge'ulah began in the night 2 since, a. Pharaoh now set them free, and b. They were free to remain in Egypt - against Pharaoh's wishes.
Gur Aryeh: Refer to 12:31:1.01:1.
What are the implications of "Kumu Tze'u... !"?
Ramban: It implies that they were to get up and leave immediately (in the middle of the night). 1
Yerushalmi Pesachim, 5:5: Pharaoh said, 'Until now you were servants of Pharaoh; 2 from now on you are servants of Hashem.' 3
Refer to 12:31:1:2**.
See Torah Temimah, note 214.
Yerushalmi (ibid.): At that moment they said, 'Halelu Avdei Hashem' - Avdei Hashem, v'Lo Avdei Pharaoh! See Oznayim la'Torah DH 'Kumu Tze'u ... ', who queries a similar Midrash, which explains that Pharaoh set them free, based on the Chazal that Pharaoh sent spies with Yisrael to make sure that they would return. Refer to 14:5:1:1.
Why did Pharaoh twice add the word "Gam" - "Gam Atem, Gam Bnei Yisrael"?
Rashi: To include both the men and the children. 1
Ramban: Pharaoh meant both Moshe and Aharon (who had brought the plagues on Pharaoh), and the Bnei Yisrael. 2
What are the implications of the word "k'Daberchem"?
Rashi: Exactly as Moshe and Aharon had requested. Pharaoh's previous statements of, 'I won't send!' (5:2), 'Who is going?' (10:8), and 'Only your sheep and cattle will remain!' (10:24), are all cancelled!
Ramban: He added the entire phrase to appease Yisrael, since they had continually asked to go out and serve Hashem. Consequently, to encourage them to leave immediately, as he now ordered them to do. 1
QUESTIONS ON RASHI
Rashi writes: "'He called [out] for Moshe and Aharon [at] night' - This tells us that [Pharaoh] went around the gates of the city, screaming, 'Where does Moshe dwell? Where does Aharon dwell?'" How is this derived?
Gur Aryeh: Do not explain that Pharaoh summoned Moshe and Aharon to appear before him (and they came). The verse emphasizes that this took place "at night" - i.e. in the unusual circumstances that the king went out at night. 1 The verse also does not say that Pharaoh 'went to' Moshe and Aharon, but rather that he "called out" for them - like a person searching for someone at night, not knowing where exactly they are.
Gur Aryeh: For someone else to answer a royal summons at night, would not be so unusual.
Rashi writes: "[Pharaoh] went around the gates of the city screaming, 'Where is Moshe?' ..." The Midrash Tanchuma tells, that the Egyptians feared that they would all be dead, by the time Bnei Yisrael finally left Egypt in the morning! So Pharaoh immediately began to announce their freedom. Why did the Makah continue hitting every Egyptian household [- even after midnight]?
Maharal (Gevuros Hashem Ch. 52, p. 225): Every Makah struck with "a strong hand" - i.e. with great force; and "an outstretched arm" - i.e. over a duration of time (so that Pharaoh would not quickly change his mind). Even Makas Bechoros, which primarily took place in one moment (at midnight), also had this prolonged aspect (i.e., in the subsequent deaths of other Mitzrim throughout the night). 1
As they later said, "We are all dying!" (12:33). For more about the terms "Yad Chazakah" and "Zero'a Netuyah" (Devarim 26:8), refer to Shemos 6:1:3.3. As for why the Redemption took place in two stages - by night and by day - refer to 12:12:2:1*.