1)
What is "Shfot"?
1.
Metzudas David: It is a judgment of punishment. Radak - this is a noun, with the grammatical form of Shmor and Yekod.
2)
Did Hashem promise this?
1.
'Rashi': Yes. After Shlomo requested this, Hashem told him "Shamati Es Tefilasecha" (7:12).
3)
Why did he say "Ki Shimcha ba'Bayis ha'Zeh"?
1.
Malbim: Due to this, Your Shechinah and Hashgachah is over us via the Mikdash, and You are prepared to save us via Tefilah in the Mikdash.


