1)
What is "Beis Hashem"?
1.
Radak: It is the house where the Aron was in Yerushalayim (before the Beis ha'Mikdash was built).
2.
Malbim: It is the Beis ha'Mikdash. The author prays to save it and all of Yerushalayim from Sancheriv, who wants to destroy it.
2)
What is "b'Sochechi"?
1.
Rashi: This is like b'Sochech (in you). Radak - the Yud is extra for clarity of the expression, like Avonaichi, Tachalu'aichi.
3)
To whom does he say "Hallelukah"?
1.
Radak: All of you should praise Hashem with me.