Why does the Torah mention Pinchas individually?
Rashi: Because he was equal to the rest of Yisrael (in Tzidkus).
Why did Pinchas go and not Elazar?
Rashi #1: Because Pinchas began to perform the Mitzvah, by killing Kozbi bas Tzur, so Hashem said 'Let him finish it!'
Rashi #2: He went to avenge the sale of his mother's great-grandfather 1 - Yosef to the Midyanim.
Rashi #3: Because he was the Kohen Gadol for war.
What were the "K'lei ha'Kodesh" which Pinchas took with him to war?
Rashi: This refers to the Aron and the Tzitz. 1
Targum Yonasan: It refers to the Urim v'Tumim. 2
What is the significance of the Tzitz? Seeing as the Kohen Gadol for war wears all eight Begadim of the Kohen Gadol, why does the Torah see fit to mention it?
Rashi: Because Bil'am, who arrived at the battle-front, 1 by means of black-magic, helped the kings of Midyan to escape, by flying away
Rashi (in Pasuk 8): in order to claim his reward for the 24,000 of Yisrael who fell at Ba'al Pe'or. He received his full reward, not from Mo'av, but from Yisrael, who paid him in full for the 24,000 (See Ba'al ha'Turim).
It is not clear however, why it is necessary to include the Aron?
Rashi: As hinted in the words "Al Chaleleihem" (in Pasuk 8), in connection with the kings of Midyan. See also, Yehoshua, 13:22.
Hashem commanded Moshe to take vengeance against Midyan. Why did Moshe himself not go?
Da'as Zekenim, Hadar Zekenim (2), Riva (2), Moshav Zekenim (4): It is because Moshe grew up in Midyan 1 . A well from which you drank water, do not throw a clump of earth in it (sully its water
Da'as Zekenim, from Bamidbar Rabah 22:4: Some say that this is not the same Midyan in which Moshe grew up. This is near Mo'av; it is desolate to this day. (The Midyan in which Yisro lived is intact.)