1)

checked Why does it mention here that the nation went home?

1.

Malbim: After David arranged the Avodah of the Aron and Mishkan, and Mishmaros of Kehunah and Leviyah, the people returned home and David blessed his house.

2)

What is "Levarech Es Beiso"?

1.

Radak (Shmuel II, 6:20): It is to give Shalom, like "Ki Simtza Ish Lo Sevarchenu" (Melachim II, 4:29).

Sefer: Perek: Pasuk:

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