What is the significance of Yaakov cursing Shimon and Levi's anger?
Rashi: Even when Yaakov was angry with his sons, he cursed, not themselves, but their anger. 1
Seforno: Their anger will be lessened via their lowliness and difficulty finding livelihood, by dividing them and scattering them among the tribes. Kehunah remained with the Bechoros until Levi earned it, following the sin of the Golden Calf. 2
Targum Yonasan: What Yaakov meant was that the town of Shechem was cursed when they attacked it to destroy it in their powerful anger, and their fury against Yosef was harsh.
Hadar Zekenim: "Arur" [here] is not a curse. It means that their anger should be diminished.
Ohr ha'Chayim: He cursed their excess anger over what is normal. He left the amount normal in people, so they will get reward in the world to come for suppressing it for Avodas Hashem. If not, they would lack an aspect of eternal happiness!
Malbim: Sometimes anger is needed, to be jealous for Hashem's honor and to punish Resha'im. However, their anger is cursed; there is no Berachah in it, for it is Az (excessive).
Ha'amek Davar: He cursed it when it is Az (fierce and unstoppable, like flooding water).
Rashi: This prompted Bil'am's statement to Balak, "How can I curse those whom Kel did not curse?" (23:8). Gur Aryeh (loc. cit.) - The term "has not cursed" (in that verse) is in past tense; to refer to a prior occasion when Bnei Yisrael where not cursed, even when it was deserved. That happened in our Pasuk. (Yaakov's Berachos were with Ru'ach ha'Kodesh - PF.)
Seforno: As the Pasuk states in Devarim 10:8.
What did Yaakov mean when he stated that he would "divide them within Yaakov, and scatter them in Yisrael"?
Rashi #1: Yaakov meant that he would separate them from one another, in that Levi would not be counted as one of the twelve tribes.
Rashi #2: He decreed that Shimon would be poor, scribes or teachers of children, 1 which would force them to scatter far and wide to find income. Levi would have to go to collect Terumos and Ma'aseros in the granaries. 2
Targum Yonasan: Part of Shimon's territory was located in the middle of Yehudah's, and part among the other tribes. 3 Levi was (given 48 towns) scattered throughout Eretz Yisrael. 4
Rashbam: By scattering Levi throughout the land, he ensured that Shimon would be separated from him.
Ohr ha'Chayim: This would cool their heat.
Malbim: There is some need for anger; I will give a small amount to each Shevet. Yisrael refers to the great of the nation; they need anger to consume Resha'im. 'Any Chacham who does not take vengeance like a snake [is not a Chacham' - Yoma 23a].
Ha'amek Davar: Sometimes there is a need for some people like this, but too many in one place is difficult. Therefore I will separate them, so there will be a few in one place. Among Yisrael (the Chasidim), sometimes such a person is needed, e.g. Pinchas in the episode with Zimri. A very small amount is good, so I will scatter them in Yisrael.
Rashi's two explanations seem to pertain to the two sections of the Pasuk, respectively (the first one to "Achalekem b'Yaakov," and the second one to "va'Afitzem b'Yisrael"). (EC)
His decree on Levi was more respectable (Rashi), presumably because of their elevated status. This in turn, may well have been rooted in the fact that, already in Egypt, they were known as righteous scholars (See Rashi and Ramban to Shemos 5:4). (EC)
Yehoshua 19:1-9 and all the Mefarshim there, including Targum Yonasan, imply that Shimon inherited only amidst Yehudah! This requires investigation. (PF) See "Erkah Shel Eretz Yisrael," by Rabbi Yehudah Landy (p. 133-134). He suggests that Shimon's inheritance amidst Yehudah was only temporary, until such time that Yehudah would grow and need to reclaim it - indeed, see Divrei Hayamim I 4:31, 4:39-43, and Divrei Hayamim II 34:6. At that later time, Shimon was scattered, and Yaakov's words were fulfilled. (CS)
See Bamidbar 35:1-8, and Yehoshua 21.
What did Yaakov hope to achieve by separating Shimon and Levi?
Targum Yonasan: As long as the two brothers remained together, no king would be able to stand up to them. 1
Is there a difference between 'Af' and 'Evrah'?
Malbim: Yes. 'Af' is against one who sinned against him. 'Evrah' is when amidst 'Af,' he sends his anger also against one who did not sin against him, and passes the limit. There was Af against Shechem ben Chamor, and Evrah against the other Anshei Shechem. Both of these were excessive, after they converted (i.e. circumcised).
Ha'amek Davar: Evrah is what is guarded in the heart.
In what way is their anger "hard"?
Ha'amek Davar: It is hard to appease them.
