What are the connotations of "Ulai Uchal Nakeh bo" mean?
Rashi #1: It means 'Let the two of us smite them'. 1
Rashi #2 and Targum Yonasan: 'Perhaps I will be able to diminish them. 2
Ramban: 'I, together with Midyan, will be able to defeat them'.
Seforno: 'Perhaps, after you curse them, we will be able to defeat them - I in battle and you, with a curse'.
Targum Yonasan: 'Perhaps I will be able tocut down their numbers and drive them out of the land!'
What did Balak mean when he said to Bil'am that whoever Bil'am blesses is indeed blessed ... ?
Rashbam: Balak knew full well that either Bil'am was a prophet and that his power lay in prophesy, or that he was a sorcerer, 1 and he only mentioned blessing and cursing here because they donkeyumed that his payers and his sacrifices too, would be effective.
Seforno: In fact, Bil'am did not have the ability to bless, 2 only to curse, 3 and Balak mentioned blessing only in deference to Bil'am, 4 so as not to convey the impression that he considered him a damager.
Seforno: Which explains why Bil'am did not ask him for an eternal B'rachah for success, or at least that he should succeed in keeping Yisrael at bay.
Seforno: By mentioning his victim's sins or because he knew the exact moment when Hashem was angry. See Torah Temimah on 23:8.
From where did Balak know that whoever Bil'am blesses is blessed ... ?
From what land did Balak want to expel Yisrael?
Da'as Zekenim, Hadar Zekenim (7): It is from his land, which Yisrael took from Sichon, who took it from Mo'av.
Why did he say "Arah Li"? It suffices to curse the nation!
Rosh: Balak knew that those who curse Yisrael are cursed (Bereishis 27:29), and through Bil'am's curse, Balak will be cursed. Even so, he wanted to do so because he loathed Yisrael so much, like Shimshon, who desired to avenge the Plishtim, even though also he would die through it (Shoftim 16:30).
Rashi writes that Balak knew that Bil'am's blessings work from the war with Sichon. He should have said, since Bil'am told him that he will become king (refer to 22:5:2:1*)!
Moshav Zekenim: Bil'am did not bless him to become king; it was a prophecy.