Why is he called "Bil'am ha'Kosem"?
Sanhedrin 106a: Initially he was a Navi. At the end (after he tried to curse Yisrael
Why is Bil'am mentioned here regarding Reuven's portion (which was from what Sichon took from Amon and Mo'av? After failing to curse Yisrael,) he returned to his land (Bamidbar 24:14)!
Radak: He counseled Mo'av and Midyan to send their beautiful daughters to have Zenus with Yisrael, and cause Hashem to be angry with them. His counsel was fulfilled, so he came to request wages from Mo'av and Midyan. 1
Abarvenel: Beis Pe'or is among Reuven's cities. Yisrael killed Bil'am for causing [through his counsel] Yisraelim to die for serving Ba'al Pe'or.
What did he request from Midyan? Balak Melech Mo'av hired him! It seems that amidst sending for him, Midyan joined forces with Mo'av against Yisrael (refer to Bamidbar 22:4:2:1). However, Bil'am was from Midyan. He did not need to come to claim wages! Why did Radak ask about Bil'am, and not about the five kings of Midyan in verse 21? They were killed in the war against Midyan, which is not connected to Reuven!
What is the meaning of "El Chaleleihem"?
Radak #1: In the Torah (Bamidbar 31:8) it says [that they killed the five kings of Midyan] "Al Chaleleihem." It is as if said "Im Chaleleihem" (with the other corpses). There are many verses like this, e.g. "va'Yavo'u ha'Anashim Al ha'Nashim" (Shemos 35:22).
Radak #2: (This is like Al Chaleleihem.) A Midrash says that the kings of Midyan did witchcraft with Bil'am, and fled Yisrael's sword and flew in the air. Pinchas showed the Tzitz to them, and they fell on their (Midyan's) corpses.
Radak #3: (This is like Al Chaleleihem.) Yisrael did to Bil'am the four Misos of Beis Din.
