What idea does this Pasuk add in the progression of the Shirah?
Maharal (Gevuros Hashem Ch. 47, p. 191): After having praised Hashem for the great and mighty blow against our enemies, we now shift focus to discuss all the good He does for Yisrael. 1
What is the correlation between the two halves of the Pasuk?
Ramban #1 (citing the Ibn Ezra): With reference to the future 1 - "You will lead with Your kindness (via the Pillars of Cloud and of Fire)... , You will lead them slowly (but surely) to the Your holy dwelling."
Seforno: The first half refers to the past - when, after taking them outside the border of Egypt to Sukos, Hashem guided them in the desert (via the two Clouds). Whereas the second half refers to the present - having led them slowly through the sea on dry land, 2 He was now leading them 3 on the journey to His holy dwelling, to sanctify them there in His service.
Ramban #2: Having discussed the fate of the Egyptians (in the previous Pasuk), the Torah now relates how Hashem saved Yisrael with the Might of His Hand - on a journey towards His holy dwelling-place.
Hadar Zekenim and Rosh: "Nachisa b'Chasdecha" is Tzedakah (Gemilus Chasadim). "Neihalta b'Ozecha" is Torah; "El Neveh Kodshecha" is the Beis ha'Mikdash (Avodah). 4
Maharal: See 15:13:3 .
Ibn Ezra: As is the way of Pesukim regarding prophecy, to discuss the future in past-tense. The Ibn Ezra himself presents an alternative explanation, which is similar to that of the Seforno in answer #2 (15:13:1:2).
Seforno: "He led them through the depths (of the sea) like a horse in the desert, to prevent them from stumbling" (Yeshayah 63:13).
Rashi: Targum Onkelos translates it as 'carrying them' (his Girsa in Targum is not 'Dabarhi' but 'Sovarhi'); whereas Targum Yonasan interprets, 'gave an inheritance to them.'
What is the Pasuk referring to when it writes, "Your holy dwelling-place"?
Rashbam: It refers to Eretz Cana'an.
"Nachisa b'Chasdecha... Neihalta b'Ozecha" ("You guided, in Your kindness... You led, in Your might"). The Mechilta comments - 'Chesed' - despite that we had no deeds with which to be worthy of it. 'Oz' - In the merit of Torah, as in the verse, "Hashem Oz l'Amo Yiten" (Tehilim 29:11); and in the merit of the Davidic kingdom, "v'Yiten Oz l'Malko" (Shmuel I 2:10). What does this Midrash mean?
Maharal (Gevuros Hashem Ch. 47, p. 191): There are two types of guidance that a person needs; a. Towards filling one's necessities - Linchos' (to guide, as in "Nachisa"). Hashem guided us (through the wilderness) with kindness, and we lacked for nothing. b. Guidance towards reaching one's potential, towards perfection - 'l'Nahel' (to lead, as in "Neihalta"). As a nation, we would reach our perfection at "Neveh Kodshecha" - "the abode of Your Sanctity," i.e. the Beis Hamikdash. 1 This would come about via the Torah; Torah is the Divine guidance that leads a person towards perfection. Also via Malchus Beis David, because a king must lead the nation to righteousness (by administering justice). Hashem would choose the dynasty of David to fulfill this. With these merits, Yisrael would achieve their national perfection - in the Beis Hamikdash.
Maharal: As we find in 'Dayeinu,' that we recite on Seder night - The final stage of the Redemption is the building of the Beis ha'Bechirah.
"Nachisa b'Chasdecha... Nei'halta b'Ozecha, El Neveh Kodshecha." The Midrash (Pesikta, 19) sees this as a refence to the "three pillars upon which the world stands - Torah, Avodah, and Gemilus Chasadim" (See Avos 1:2). How so?
Maharal (Gevuros Hashem Ch. 47, p. 191): As above (see 15:13:3:1 ) - "Ozecha" alludes to Torah; "Chasdecha" is the trait of Gemilus Chasadim; and "Neveh Kodshecha" is the Beis Hamikdash, where the Avodah would be performed. Bnei Yisrael left Egypt in a state of connection and attachment to Hashem. There are three aspects of this connection; a. Hashem bestows His Chesed upon the world, 1 thus he attaches Himself to us (in Maharal's terms, 'Deveikus Ilah be'Alul'). b. When man desires to serve Hashem with Avodah, man attaches himself to Hashem ('Deveikus Alul b'Ilah'). c. The Torah itself is the medium by which both Hashem and man connect together; that is why Torah is called a Bris. Were it not for these three aspects of connection, the world would falter. At the Exodus, Yisrael had already established these three connections. They would reach full completion, and support the entire world, upon reaching the Beis Hamikdash. 2
Maharal asks (Derech Chayim p. 28, to Avos 1:2): We usually understand 'Gemilus Chasadim' to mean that the kindnesses that people do for each other, is what supports the world; whereas our verse speaks of Hashem's Chesed to Man! Maharal answers that when people perform Chesed for each other, Hashem reciprocates with Chesed from Above. Compare to Maharal in Gevuros Hashem (Ch. 46, p. 176).
Maharal (ibid. p. 27): The world stands upon, a. the beneficence of Hashem's kindness; b. The world was created for the purpose of service of Hashem. (Intrinsic existence is Hashem's alone; everything else exists through their service of Him.) c. The world is complete, it is not meaningless existence (Tohu). This completion comes about through Torah.