(11)Only the males among Aaron’s descendants may eat of it, as their due for all time throughout the ages from GOD’s offerings by fire. Anything that touches these shall become holy.

(12) Moses spoke to Aaron and to his remaining sons, Eleazar and Ithamar: Take the grain offering that is left over from GOD’s offerings by fire and eat it unleavened beside the altar, for it is most holy. (13) You shall eat it in the sacred precinct, since it is your due, and that of your sons, from GOD’s offerings by fire; for so I have been commanded. (14) But the breast of elevation offering and the thigh of gift offering you [and your wife], andyour sons and daughters with you, may eat in any pure place, for they have been assigned as a due to you and your sons from the Israelites’ sacrifices of well-being.

(22) GOD spoke to Moses: (23) Speak to Aaron and his sons: Thus shall you bless the people of Israel. Say to them: (24) GOD bless you and protect you!(25) GOD deal kindly and graciously with you! (26) GOD bestow favor upon you and grant you peace! (27) Thus they shall link My name with the people of Israel, and I will bless them.

A dilemma was raised before the Sages: What is the halakha with regard to elevating from the lifting of hands for the Priestly Benediction to priestly lineage? Is the presumptive status of a person who recites the Priestly Benediction in the synagogue that of a priest in terms of lineage as well? The Gemara notes: Raise the dilemma according to the one who said: One elevates from teruma to lineage; and raise the dilemma according to the one who said: One does not elevate from teruma to lineage. The Gemara notes: Raise the dilemma according to the one who said: One elevates from teruma to lineage. In his opinion, perhaps this applies only to teruma, where a non-priest who partakes of teruma performs a transgression whose punishment is death at the hand of Heaven. One would not partake of teruma and risk that punishment if he were not a priest. However, with regard to the Priestly Benediction, where a non-priest who recites it violates a prohibition stated as a positive mitzva, no, one cannot be certain that one would not recite the blessing if he were not a priest. Therefore, one does not elevate from the lifting of hands to priestly lineage. Or, perhaps there is no difference, and in both cases because there is a transgression involved one can assume that he would not risk performing a transgression were he not a priest...

And Rabbi Yosei said: In all my days I never violated the words of my friends. I know about myself that I am not a priest, and nevertheless, if my friends say to me: Go up to the platform with the priests, I go up.

Rema

(Tosafot in the chapter "Kol Kitvei" [Shabbat, ch. 16] states that the R"i does not know what prohibition there would be for a non-Kohen who ascends [for Birkat Kohanim], and it is possible that along with others who are Kohanim [it would be permitted]; but this requires further consideration).

Rema

A non-Kohen should not "raise the hands", even along with (others who are Kohanim).

When a non-priest serves in the Temple, his service is invalid and he is liable for death at the hand of heaven, as [Numbers 18:7] states: "A non-priest who draws close will die."...
What is meant by a non-priest? Anyone who is not a male descendant of Aaron, as [Leviticus 1:8] states: "And the sons of Aaron shall arrange" and [Leviticus 3:8] states: "And the sons of Aaron shall set afire." [These service are performed by] "the sons of Aaron" and not the daughters of Aaron.

(12) If a priest’s daughter becomes a layman’s wife, she may not eat of the sacred gifts; (13) but if the priest’s daughter is widowed or divorced and without offspring, and is back in her father’s house as in her youth, she may eat of her father’s food. No lay person may eat of it— (14) but if someone eats of a sacred donation unwittingly, the priest shall be paid for the sacred donation, adding one-fifth of its value.

(2) If the daughter of a priest married an Israelite and afterwards ate terumah, she must repay the value but not the fifth...

§ Rav Adda bar Ahava says: With regard to the daughter of a Levite who gave birth to a firstborn boy, her son is exempt from the obligation to give five sela coins to the priest for his redemption, as the child is considered to be the son of a Levite and Levites are exempt from this obligation. The Gemara asks: From whom did she become pregnant? If we say that she became pregnant from a priest or a Levite, why does Rav Adda bar Ahava refer specifically to the daughter of a Levite? The halakha would be the same even for an Israelite woman who became pregnant from a priest or a Levite. Rather, Rav Adda bar Ahava must be referring to a case where the daughter of a Levite became pregnant from an Israelite. But if so, why is the son’s status determined by his mother’s status in this instance? After all, it is written: “By their families, by their fathers’ houses” (Numbers 1:2), which indicates that the lineage of a Jewish family follows the father rather than the mother. Rav Pappa says: This is referring to the daughter of a Levite who became pregnant from a gentile. In such a case, the son’s status is determined by that of the mother, and therefore the son is exempt from the redemption of the firstborn. And do not say this is the halakha only according to the one who says that in such a situation one does not disqualify the child at all due to his gentile father, and he is of fit lineage. Rather, even according to the one who says that one does disqualify the child due to the gentile father, nevertheless, one also follows the mother and he is therefore called a Levite of flawed lineage, and is exempt from redemption. Mar, son of Rav Yosef, says a different explanation, in the name of Rava: Actually, Rav Adda bar Ahava is referring to a case where the daughter of a Levite became pregnant from an Israelite. And although the son’s status is usually determined by that of the father, there, with regard to the redemption of the firstborn, it is different, as the verse states: “Whatever opens the womb among the children of Israel” (Exodus 13:2). This teaches that the Merciful One renders the obligation dependent upon the opening of the womb, and since this firstborn came from the womb of a daughter of a Levite, and not a Levite, the obligation of redemption does not apply.

Similarly, the redemption of firstborn [sons is given] only to males of the priestly family, for concerning it, [Numbers 3:48] states: 'And you shall give the money to Aaron and his sons.'

Anyone who partakesof terumah should recite the blessing for that particular food and then recite the blessing: "[Blessed are You... who has sanctified us with the holiness of Aaron and commanded us to partake of terumah."...