If, as the Sifri explains, Aharon was commanded to bless the people with Birkas Kohanim, why does the Torah repeat it here?
Ramban: The command there was with the setting-up of the Mishkan, "where Hashem has commanded the Berachah of life forever" (Tehilim, 133:3); There, the blessing was with the full Name of Hashem, elsewhere, it was with one of Hashem's Kinuyim; There it was said as one Berachah; elsewhere, as three (Yevaresh'cha, Ya'er, Yisa. See R. Chavel's footnotes.)
What are the connotations of the phrase "Koh Sevarchu ... "?
Rashi (Kesuvos, 24b): The Torah is confining blessing the people to the Kohanim, placing an Isur Asei on a Zar who blesses the people. 1
Rashbam: With reference to the following Pesukim, the Kohanim should not bless the people in an abstract manner, as Reuven wishes blessings 'to fall upon Shimon's head', but request from Hashem that He should bless them. 2
Targum Yonasan: The Kohanim should bless Yisrael 3 'with spread-out hands, on the Duchen and using the exact words that the Torah uses - "Yevarech'cha... "
Torah Temimah: "Koh Sevarchu" - in Lashon ha'Kodesh, with hands spread-out (Sotah, 38a). 4
Hadar Zekeinim: This is a Mitzvas Aseh. A Kohen who does not ascend to bless transgresses an Aseh (Sotah 38b), i.e. if they told him 5 to ascend, for it says "Amor Lahem."
Since a prohibition that is based on an Asei is an Asei.
Rashbam: Because then Hashem will respond accordingly, as stated in Pasuk 27.
See Peirush Yonasan.
See Sotah, 38a. See also Ba'al ha'Turim.
Moshav Zekeinim (27): The Yerushalmi (Brachos 5:4) proves so. When R. Elazar's head hurt, he went outside the Beis ha'Keneses (since he was not told to ascend, he does not transgress).
What are the implications of "Amor lahem"?
Rashi: It implies that when the Kohanim bless Yisrael, they should bless them loudly and clearly, so that everybody can hear them.
R. Bechayei: The Shali'ach Tzibur must say each word, and the Kohanim say after him. 1
Refer to 6:23:2:5.
Olas Tamid (128:4): A Zar who blesses, even together with Kohanim, transgresses. Refer to 6:23:2:1.
R. Bechayei: The Brachah comes from above to the Shali'ach Tzibur, then to the Kohanim, and then to the Tzibur.
Why is "Amor" written Malei (with a 'Vav')?
Rashi (from Tanchuma 18): To teach that the Kohanim should not bless Yisrael quickly in a hurried tone, but slowly and with Kavanah. 1
Minchas Shai (citing the Zohar): This makes its Gematriya 247; the other 247 limbs of the body depend on one of them, and all are blessed through the three verses of Birkas Kohanim.
Minchas Shai, citing Mordechai (Megilah 816): We put the Vov from Amor into Cho, to make it Kavah (window; refer to 6:23:152:1).
Rosh (Brachos 5:17): Refer to 6:23:3:2.
Imrei Emes, citing Megaleh Amukos: Birkas Kohanim includes all Brachos in the world. They will be fulfilled only in the future, when "Toldos" will be full.
Riva, citing a Midrash: It is Chaser (without a 'Vav') to teach that the Shali'ach Tzibur answers Amen to each Brachah. We infer that only the Shali'ach Tzibur calls them. 2
See also Ba'al ha'Turim.
I.e. if another could call them, we would not let the Shali'ach Tzibur do so, for it is like an interruption in Chazaras ha'Shatz. How does this teach that he answers Amen? Perhaps the text should say 'it is Malei'; I did not find anyone else say that it is Chaser. Or, it should say that he does not answer Amen, like Tanchuma (Vayechi 7 - PF).
Why is Birkas Kohanim taught right after Nazir?
Moshav Zekeinim (11) #1: This hints that one who drank wine may not Duchan (give Birkas Kohanim). However, one who ate Chartzan is permitted. "Lesharso u'Levarech bi'Shmo" (Devarim 10:8) - a Kohen who serves is permitted Chartzan and forbidden wine, also one who blesses. One might have thought that just like a Kohen Ba'al Mum may not serve, he may not Duchan - the Hekesh to Nazir refutes this. 1
Moshav Zekeinim (11) #2: Kedushas Nazir is like a Kohen Gadol - he is not Metamei even for relatives
Moshav Zekeinim: Megilah (24b) forbids a Kohen with Mumim on his hands to Duchan, for people look at him! The Tosefta says that this is only Mumim on his hands and face, but other Mumim do not disqualify him. Even on his hands and face, he is permitted in his city, for people are used to him and will not look at him.
Why is "Cho" written Malei (with a 'Vav')?
Moshav Zekeinim: This 1 hints to a window; the Targum is Kavah, like "Mashgi'ach Min ha'Chalonos" (Shir ha'Shirim 2:9), i.e. between the fingers of the Kohanim. When they lift their hands, they make like a window. 2
Why is Birkas Kohanim needed? Tzadikim are already blessed "Im b'Chukosai Telechu", and Resha'im are cursed in the two Tochachos!
Moshav Zekeinim citing R. Yehudah ha'Chasid: It is for Tzadikim. There are many Resha'im who have a Mazal that their curses work even on Tzadikim. Birkas Kohanim saves them from their curses.