What is the meaning of "Moshivi Akeres ha'Bayis"?
Pesachim 118b: [The most pious part of] Keneses Yisrael says to Hashem, Your children [through their sins in exile] made me [lowly] like a weasel that dwells in IKaRei Batim (underneath houses).
Rashi: Tziyon, which is [now] like a barren woman, [He] will make it settled.
Radak: He reverses nature. He establishes Akeres ba'Bayis 1 , i.e. she will have children. This is like "va'Ya'as Lahem Batim" (Shemos 1:21), "Moshiv Yechidim Baysah" (above, 68:7).
Malbim: Also a woman who drank a sterility potion (for her husband desired her beauty, and did not want her to become pregnant), He will cure her with His Hashgachah, until she will be a happy mother of children.
Radak: Sometimes it says Akeres (and not Akarah), even though it is not Samuch. Also other words are like this - Atarah or Ateres, Mamlachah or Mamleches, Milchamah or Milchemes.
Why does it say "Em ha'Banim Semechah"?
Rashi: "Ki Chalah Gam Yaldah Tziyon Es Baneha" (Yeshayah 66:8).
Radak: Now she will be happy with her children - in place of being sad without them.
Why does it conclude "Hallelukah"?
Radak: For all of these wonders that Hashem does you are obligated to praise Him.
