Why does the Torah add the (otherwise superfluos) word "me'Echav"?
Horayos, 12b: To teach us a. that the Kohen Gadol should be greater than his brothers 1 and b. that if he is poor, they should enrich him. 2
Moshav Zekenim: As hinted in the letters of "ha'Gadol" which spell 'Gadleihu' ('Make him great!'). He must be greater than them, since he is greater even than Micha'el, the great minister, as the Pasuk indicates in Acharei-Mos, 16:17 "ve'Chol Adam Lo Yih'yeh be'Ohel Mo'ed be'Vo'o" - even than the angels, about whom it is written in Yechezkel 1:10 "u'Demus P'neihem P'nei Adam". See also Oznayim la'Torah DH 've'ha'Kohen ha'Gadol me'Echav' #2, who elaborates.
In which regards is the Kohen Gadol superior to his fellow Kohanim?
Ba'al ha'Turim and Moshav Zekenim (citing Midrash Rabah): He is superior to them in five ways 1 : In looks, in strength, in wealth 2 , in wisdom and in age.
Yoma, 18a: In strength, in beauty, in wisdom and in wealth.
Ba'al ha'Turim: As hinted in the 'Hey' of "ha'Gadol."
Refer to 21:10:0.1:1 and note #2.2. And the Torah Temimah, citing the Sifra, adds 'in appearance', and citing the Yalkut, 'in stature'. See Torah Temimah, note 64.
Having written "ha'Kohen ha'Gadol me'Echav", why does the Torah see fit to add the descriptions that follow "asher Yutzak al Rosho Shemen ha'Mishchah ... "?
Horayos, 12b: "Asher Yutzak al Rosho Shemen ha'Mishchah incorporates Mashu'ach Milchamah and "u'Milei Es Yado Lil'bosh Es ha'Begadim", the Kohen Gadol Merubeh Begadim (who was inaugurated by wearing the Bigdei Kohen Gadol) 1 in the current Halachos.
Oznayim la'Torah: To teach us that, if the Kohen Gadol dies and his son inherits his position, he does not have the Din of a Kohen Gadol until he is anointed with the Shemen ha'Mishchah or wears the Begadim of a Kohen Gadol 2 - and is therefore permitted to bury his deceased father.
Why does the Torah write "Yutzak al Rosho" and "Milei Es ha'Begadim" in the third person?
Oznayim la'Torah: Because the anointing was performed by a Navi and the appointment and wearing the Bigdei Kehunah, by the Sanhadrin, 1 and not of his own accord.
See Oznayim la'Torah, who elaborates.
What is the meaning of "es Rosho Lo Yifra?
Rashi: It means that the Kohen Gadol is not permitted to let his hair grow long 1 (as a sign of mourning - refer to 21:10:3:1**).
Rashi: A growth of thirty days. See Sifsei Chachamim. Moshav Zekenim - Mo'ed Katan (24a) expounds that a different Aveil who does not grow his hair long or tear his clothes will be Chayav Misah. (We know that an Aveil is forbidden to cut his hair for thirty days. Really, the Gemara learned from 10:6, but also there, even Aharon's sons had the law of a Kohen Gadol - refer to 10:6:1:2, 10:6:1:2 2
. - PF)
What is the meaning of "u'Vegadav Lo Yifrom"?
Why is the Kohen Gadol not permitted to let his hair grow long and to rent his garments as a sign of mourning for his deceased relatives?
Oznayim la'Torah: In order not to defile the Shamen ha'Mishchah with which he was anointed and in order not to spoil the holy garments. 1
See Oznayim la'Torah. Nor is he permitted to leave the Beis-Hamikdash and to change into Bigdei Chol, since the Torah writes, in Pasuk 12 "u'Min ha'Mikdash Lo Yeitzei" (Oznayim la'Torah,)