Why does it say "ha'Par ha'Chatas"?
Radak: Sometimes the prefix Hei ha'Yedi'ah (to identify) appears even on a Samuch (compound noun), e.g. "ha'Mizbe'ach ha'Nechoshes" (Melachim II, 16:14).
Where is "b'Mifkad ha'Bayis"?
Targum Yonasan: In a place proper for the Bayis. Rashi ? i.e. in a Kadosh place. Mifkad ha'Bayis is a place where the Bayis is finished, like "v'Lo Nifkad Mimenu Ish" (Bamidbar 31:49). Radak ? the Targum did not say where.
Radak: This is like b'Mitzvas, like "v'Hu Fakad Alai" (Ezra 1:2), "b'Mifkad Chizkiyah" (Divrei ha'Yamim II, 31:13). I.e. in a place in the Bayis where they are commanded to burn Parim ha'Nisrafim and Se'irim ha'Nisrafim (Korbanos brought when most of Yisrael transgressed an Isur Kares due to a mistaken ruling of the Great Sanhedrin). Also Moshe's bull in the Milu'im and the calf that Aharon offered on the eighth day were burned.
Malbim: It is a place designated for burning what must be burned.
Where is "mi'Chutz la'Mikdash"?
Radak: It is outside the Azarah, but inside the wall of Har ha'Bayis.
Malbim: This is like Par ha'Milu'im of Chanukas ha'Mishkan which was burned "mi'Chutz la'Machaneh" (Shemos 29:14).