What are the ramifications of "B'ris Kehunas Olam"?
Rashi: Pinchas was granted a permanent lease of Kehunah for himself and his offspring.
Targum Yonasan: 'Because they denigrated him by calling him the son of Puti the Midyanite, 1 I will bestow upon him the Kehunah Gedolah, and because he took the spear with his arm, struck the Midyanite woman in her womb and prayed with his mouth on behalf of the people of Yisrael, the Kohanim will receive the three gifts- the right foreleg, the jaws and the stomach.
Hadar Zekenim: He became Mashu'ach Milchamah from now and onwards. Da'as Zekenim - he was not a Kohen until now.
Rashi writes that Pinchas became a Kohen only now. Why was he not already a Kohen?
Rashi: Because he was already born when Aharon and his sons were chosen to become Kohanim, and it was only their subsequent offspring who continued the line of Kehunah. 1
Da'as Zekenim, Hadar Zekenim (14): The Milu'im was only for Aharon and his sons (but not his grandsons), and Bigdei Kehunah were made only for them.
What is the meaning of "asher Kinei l'Elokav"?
Rashi: It means 'because he was zealous on behalf of 1 his G-d'.
What is the connection between Pinchas' zealousness on behalf of his G-d and the B'ris Shalom that he received as a reward?
Seforno:Since Pinchas quarreled Hashem's quarrel, Hashem saved him from the quarrel of competing forces. 1
Toldos Yitzchak: Because he killed esteemed people from great families, and he could be in danger. (The Bris Shalom assured him that he need not worry.)
What is the significance of the statement "Vayechaper al Bnei Yisrael"? Did he offer a Korban?
Seforno: Because he atoned for Yisrael, by killing the adulterers in public in order that the people should receive atonement by not objecting 1 to his actions, he received the Kehunah, granting him a mandate to atone for the people.
Rosh: This teaches that one who kills Resha'im, it is as if he offered a Korban.
Da'as Zekenim: He is proper to make other Kaparos (offer Korbanos) for Yisrael.
Why does it say "Bris Kehunas Olam", and "Brisi Shalom"? Regarding Aharon, it says "Lo ul'Zar'o Acharav Kehunas Olam"?
Moshav Zekenim: Pinchas received "Brisi Shalom", i.e. a Bris with Shalom attached, as a reward for Kin'as Hashem. Aharon had received Kehunah "l'Chavod ul'Sifares. (Shemos 28:2)."