Whereabouts on the Kohen Gadol's head was the Tzitz worn?
Refer to 28:37:2:1 & 2.
Targum Yonasan (on Pasuk 37): It was worn on the Mitznefes above the Tefilin shel Rosh. 1
This cannot however, be understood literally, since the Torh specificzlly states tha it was worn on the Kohen Gadol's forehead. See Na'ar Yonasan.
Which sin did the Tzitz atone for?
Rashi: It atoned for the blood or the Chalavim 1 of Korbanos that were brought be'Tum'ah, 2 as implied by "Avon ha'Kodashim".
Rashbam: It atoned for any sin on which one brings an Olah, a Chatas or an Asham to atone - together with the respective Korban.
Targum Yonasan #1: It atoned for the abuse (Me'ilah) of Hekdesh.
Targum Yonasan #2 (in Pasuk 37) and Erchin, 16a: It atones for Chutzpah. 3
But not for Kohanim who brought Korbanos (or who ate Kodshim - Rashi Pesachim, 16b) when they were Tamei.
And not for the sin of Pigul or Nosar (See Rashi). Because Tum'ah has the leniency that it can be brought be'Tzibur (Torah Temimah). See also Torah Temimah, citing Menachos, 25a, and notes 21 & 22.
Which explains why it is worn on the Kohen Gadol's forehead ('Metzach' - since Chutzpah is also known as 'Azus Metzach') See also Peirush Yonasan. By the same token, the Gemara in Erchin (16a) points out that each of the Kohen Gadol's Begadim atoned for a specific sin ... The tunic for murder, The pants for adultery, The hat (turban) for arrogance, The belt for immoral thoughts, The Choshen Mishpat for perversion of justice, The Eifod for Avodah-Zarah, The Me'il for Lashon-ha'Ra and The Tzitz for Chutzpah. See Torah Temimah, in Pasuk 39, citing Zevachim, 88b. for sources, and notes 4 & 5.
What if the Kohen Gadol was not wearing the Tzitz?
Yoma, 7b: The Tzitz only atoned whilst the Kohen Gadol was wearing it, as implied by the Pasuk. 1
This does not create a problem with the occasions on Yom Kipur when he only wore the four Begadim - since all the Avodah on Yom Kipur was Avodas Tzibur which did not require Ritzuy Tzitz (Torah Temimah).
Wha are he implications of the word "Ve'hayah al Mitzcho"?
Menachos, 8a: It implies that the Tzitz must be whole (unbroken). 1
It is possibble that the Gemara learns it from the fact that the Torah repeats the words "Ve'hayah al Mitzcho". See also Torah Temimah, note 25. The Gemara here also extrapolates from the words "Al Mitzcho" that the Tzitz should always be on the same location. See Torah Temimah, note 24.
What are the implications of the word "le'Ratzon lahem"?
Yevamos, 60b: It implies that the Tzitz will not respond to anything punitive concerning Yisrael ("lahem"), but it will if it concerns Nochrim. 1
Zevachim, 45b: It implies that the Tzitz only atones for a Yisrael (who brings a Korban be'Tum'ah), but not for Nochrim, who are not subject to the goodwill of Hashem.
Such as a question whether to kill a Yisrael or not. See Torah Temimah, note 27.
Bearing in mind that the Kohen Gadol only wore the Tzitz whilst performing the Avodah, why does the Torah insert the word "Tamid"?
Rashi #1 (citing Yoma, 7b): To teach us that the Tzitz atones even when the Kohen Gadol is not wearing it.
Rashi #2 (Ibid.), according o the opinion that confines Rizuy Tzitz to where the Kohen Gadol is wearing it. 1 To instruct the Kohen Gadol to constantly touch it, in order not to take his mind off it. 2
Menachos, 7b: To each the Kohen Gadol never to take his mind off it. 3
Like we do regarding Tefilin. Rashi: This explanation coincides with the opinion cited earlier. Refer to 28:38:1.1:1.
Refer to 28:38:1.1:1.
See answer #2 and orah Temimah, note 26.
