Where do they cook?
Malbim: In Chatzeros Keturos, like it says below (22). They are in the corner of Chatzer ha'Chitzonah. It did not receive Kedushas Azarah.
Why does it specify Chatas and Asham?
Radak: Kohanim eat their meat.
What is the meaning of "l'Vilti Hotzi"?
Rashi: This is like Lehotzi (to take out). Kodshei Kodoshim are disqualified if they leave [the Azarah].
What is "he'Chatzer ha'Chitzonah"?
Radak #1: It is Ezras Yisrael, like it says "v'Al Yetz'u meha'Mikdash El he'Chatzer ha'Chitzonah" (42:14). Just like they were warned not to go out to the Chatzer in Bigdei Kehunah, so they are warned not to take meat of Kodshei Kodoshim and Minchah there; they are disqualified via leaving their place. Even though taking them to Ezras Yisrael does not disqualify them, for it is Kadosh for eating Kodshei Kodoshim, it would seem that also Yisrael are allowed to eat them.
Radak #2: It is Ezras Nashim. Kodshei Kodoshim are disqualified if taken out to there.
What is the meaning of "Lekadesh ha'Am"?
Rashi citing Targum Yonasan: To mix with the nation. Radak ? i.e. Yisrael will think that they may eat Kodshei Kodoshim brought there.
Malbim: This is a metaphor ? taking Kodesh out of its boundary to the Am and Chol, it is as if Kedushah is uprooted from the Kodesh to the Am and Chol - "v'Lo Yekadshu Es ha'Am b'Vigdeihem" (44:19).
Why does it say "Asher Yofu Es ha'Minchah"?
Radak: It means va'Asher Yofu Sham Es ha'Minchah. Also it is called Kodesh Kodoshim (Kohanim must eat it in the Azarah).