Why does it say "Kol Tefilah v'Chol Techinah"?
Malbim: This includes all kinds of prayers - whether through request or supplication.
Why did he say "l'Chol Adam ul'Chol Amcha Yisrael"?
Radak, Malbim: It is both for individuals who need salvation, and the Rabim.
What is the meaning of "Asher Yed'un Ish Nega Levavo"?
Radak: Every man according to his affliction that he knows, but others do not know. I.e. both hidden pains and open pains.
Malbim: Even regarding a public affliction, e.g. famine or a plague, and one knows his own sin or his own needs.
Why did he say "El ha'Bayis ha'Zeh"?
Radak #1: This is like ba'Bayis ha'Zeh. I.e. he will spread his hands to Hashem in this house.
Radak #2: Whenever he is, he will spread his hands towards this house.