(ו) כֹּהֵן שֶׁלֹּא הָיָה לוֹ דָּבָר מִכָּל אֵלּוּ הַדְּבָרִים הַמּוֹנְעִין נְשִׂיאַת כַּפַּיִם אַף עַל פִּי שֶׁאֵינוֹ חָכָם וְאֵינוֹ מְדַקְדֵּק בְּמִצְוֹת אוֹ שֶׁהָיוּ הַבְּרִיּוֹת מְרַנְּנִים אַחֲרָיו אוֹ שֶׁלֹּא הָיָה מַשָּׂאוֹ וּמַתָּנוֹ בְּצֶדֶק הֲרֵי זֶה נוֹשֵׂא אֶת כַּפָּיו וְאֵין מוֹנְעִין אוֹתוֹ לְפִי שֶׁזּוֹ מִצְוַת עֲשֵׂה עַל כָּל כֹּהֵן וְכֹהֵן שֶׁרָאוּי לִנְשִׂיאַת כַּפַּיִם וְאֵין אוֹמְרִים לְאָדָם רָשָׁע הוֹסֵף רֶשַׁע וְהִמָּנַע מִן הַמִּצְוֹת:
(ז) וְאַל תִּתְמַהּ וְתֹאמַר וּמַה תּוֹעִיל בִּרְכַּת הֶדְיוֹט זֶה. שֶׁאֵין קִבּוּל הַבְּרָכָה תָּלוּי בַּכֹּהֲנִים אֶלָּא בְּהַקָּדוֹשׁ בָּרוּךְ הוּא שֶׁנֶּאֱמַר (במדבר ו כז) ״וְשָׂמוּ אֶת שְׁמִי עַל בְּנֵי יִשְׂרָאֵל וַאֲנִי אֲבָרַכֶם״. הַכֹּהֲנִים עוֹשִׂים מִצְוָתָן שֶׁנִּצְטַוּוּ בָּהּ וְהַקָּדוֹשׁ בָּרוּךְ הוּא בְרַחֲמָיו מְבָרֵךְ אֶת יִשְׂרָאֵל כְּחֶפְצוֹ:
(6) A priest who is free from any of these disqualifications (Six things prevent the performance of the rite of the Priestly Benediction: Defective speech; Physical blemishes; Transgressions; Wine; Age; Uncleanliness of the hands)...even though he is not a scholar nor punctilious in the observance of religious duties, and even though people talk about him and his dealings are not marked by strict integrity, nevertheless pronounces the Priestly Benediction and should not be prevented from performing the rite; since it is a duty incumbent on every qualified priest to bless the people, and we do not say to a wicked man, "Be still more wicked and abstain from fulfilling religious duties."
(7) Do not wonder and say, "Of what use is the blessing of this ordinary person?" The acceptance of the Benediction does not depend upon the priest but upon the Almighty, as it is said, "So shall they put My name upon the children of Israel, and I will bless them" (Numbers 6:27). The priests fulfill their duty with which they have been charged, and the Almighty, in His mercy, blesses Israel according to His will.
(י) הֶחָמֵשׁ שֶׁבִּירוּשָׁלַיִם הֵן קָדָשִׁים קַלִּים וְנֶאֱכָלִין לִזְכָרִים וְלִנְקֵבוֹת וּבָהֶן נֶאֱמַר (במדבר יח יא) "לְךָ נְתַתִּים וּלְבָנֶיךָ וְלִבְנֹתֶיךָ אִתְּךָ לְחָק עוֹלָם". וְאַף עַל פִּי כֵן אֵין נִתָּנִין אֶלָּא לְזִכְרֵי כְּהֻנָּה שֶׁהֲרֵי לְאַנְשֵׁי מִשְׁמָר הֵן. וְהַבְּכוֹר מַקְרִיבִין חֶלְבּוֹ וְדָמוֹ וְאֵין מַקְרִיבוֹ אֶלָּא אִישׁ. וְכֵן עוֹרוֹת קָדְשֵׁי הַקָּדָשִׁים. וּשְׂדֵה אֲחֻזָּה. וְהַחֲרָמִים. וְגֵזֶל הַגֵּר. אֵין זוֹכִין בָּהֶן אֶלָּא אַנְשֵׁי מִשְׁמָר כְּמוֹ שֶׁיִּתְבָּאֵר. וכן פדיון הבן לזכרי כהונה...
The five (offerings) that are only eaten in Jerusalem are offerings of 'minor' holiness and are eaten by males and females as it says, "To you I gave them, to your sons and your daughters for you forever." And in spite of this they are only given to male kohanim since they serve in a priestly role...and similarly redemption of the first born should be performed by male kohanim...
Tosfot: Female kohanim may perform redemption of the first born.(Tosfot to Pesachim 49a)
Rabbi Joel Roth, "Surely according to Tosafot and the Rosh in Rashi's name, pidgin haben is another indication of lineal sanctity for the daughters of Priests even if married. It is equally important to note that Maimonides' view does not either preclude or deny lineal sanctity to daughters of Priests. This exclusion from the right to redeem is based on the biblical statement 'for Aaron and his sons'." (From The Status of Daughters of Kohanim and Leviyim for Aliyot)
'Thus shall you bless' - women are included, plural, and 'your children' (banav) refers sometimes to 'descendants' not only sons.(Rabinowitz te'shuvah) As in Isaiah 54:13, "All your children, students of Ado-nai, and great will be the peace of your children." Metzudat David & Metzudat Tziyon, 'students of Ado-nai', Radak: 'Everyone will know Me, from the youngest to the oldest.'
(א) "ושמו את שמי" - למה נאמר? לפי שהוא אומר "כה תברכו את בני ישראל" - בשם המפורש. אתה אומר בשם המפורש או אינו אלא בכינוי? תלמוד לומר "ושמו את שמי". במקדש בשם המפורש, במדינה בכינוי (סוטה לג). "ואני אברכם" - למה נאמר? לפי שהוא אומר "כה תברכו", אין לי אלא ברכה לישראל, ברכה לכהנים מנין? תלמוד לומר "ואני אברכם". "ואני אברכם" - שלא יהיו ישראל אומרים ברכותיהם תלויות בכהניהם, תלמוד לומר "ואני אברכם". שלא יהיו הכהנים אומרים אנו נברך ישראל, תלמוד לומר "ואני אברכם". אני אברך את עמי ישראל, שנאמר (דברים טו): "כי יי אלקיך ברכך בכל מעשה ידך כאשר דבר לך". ואומר (דברים כח): "ברוך תהיה מכל העמים". ואומר (דברים כח): "יפתח יי לך את אוצרו הטוב את השמים". ואומר (יחזקאל לד): "במרעה טוב ארעה אותם". ואומר (יחזקאל לד): "אני ארעה את צאני".
(1) (Bamidbar 6:27) "And they shall place My name": Why is this stated? It is written (Ibid. 23) "Thus shall you bless the children of Israel" — with the explicit Name (the Tetragrammaton). — But perhaps with an epithet (only). It is, therefore, written "And they shall place My name" — My distinctive name (Yod-Keh-Vav-Keh). I might think, even in the borders (of Jerusalem). It is, therefore, written here "And they shall place My name," and elsewhere (Devarim 12:5) "to place My name there." Just as there, the Temple; here, too, the Temple. In the sanctuary, with the explicit Name; in the province, with an epithet. "and I shall bless them": Why is this stated? (Ibid. 23) "Thus shall you bless, etc." tells us only of a blessing [by the Cohanim] to Israel. Whence do I derive a blessing for the Cohanim themselves? From "and I shall bless them." Variantly: "and I shall bless them": So that Israel not say that their blessings are dependent upon the Cohanim; it is written "and I shall bless them." So that the Cohanim not say We shall bless Israel, it is written "and I shall bless them." I shall bless My people Israel, as it is written (Devarim 2:7) "For the L-rd your G-d has blessed you in all the work of your hands," (15:6) "as He spoke to you," viz. (7:13) "And He will love you and bless you and multiply you, and bless etc.", and (28:12) "The L-rd will open for you His goodly treasure, the heavens," and (Ezekiel 34:14) "In a goodly pasture will I graze them," and (Ibid. 15) "I will feed My flock."
According to the Rabinowitz te'shuvah:
Evolution of Nesiyat Kapayim - Priestly Blessing:
1. Performed in the Temple and outside the Temple as well.
2. After the destruction, the blessings takes place in the synagogue.
3. Later, additional phrases were added to be recited by the congregation.
4. In the absence of Kohanim, the leader recited the blessings.
The biblical verses make no mention of location for the blessing (Temple vs. not in Temple), no reference to time or place.
Also, the discussion in Talmud, Ta'anit 26b suggests that the priestly blessing is not a prayer limited by time (she'ha'zman gra'ma) a category of mitzvoth to which women were traditionally not obligated. According to the discussion, the halacha follows Rabbi Meir argues we include the priestly blessing from shacharit (the morning service) all the way through Ne'ilah.
Summary of the Bramnick & Kogen te'shuvah:
"If the priestly blessing is to be regarded as a continuation of a Temple ritual, it should be performed only by the descendants of Aaron who would have been eligible to perform it in the Temple."