Seeing as Hashem had permitted Bil'am to go, why was He angry with him for going?
Rashi: Because he wanted to go, in spite of the fact that it was evil in the Eyes of Hashem. 1
Ramban: Refer to 22:20:1:3. And Hashem was angry with him for not telling the emissaries what Hashem had said. By wordlessly saddling his donkey and accompanying them, 2 he created a Chilul Hashem, conveying the impression that Hashem had changed His mind and now agreed to curse Yisrael. Moreover, when later, they would see that he would not curse Yisrael, they would accuse Hashem of poking fun at them.
Da'as Zekenim, Hadar Zekenim, Targum Yonasan: Because he went with the intention of cursing Yisrael - even though Hashem had only permitted him to go on condition that he say whatever He tells him to (Da'as Zekenim - for the sake of wages).
Moshav Zekenim, Riva (22): Hashem permitted him to go with them, but not alone, lest he engage in divining (Ohr ha'Chayim 22
Moshav Zekenim: And Hashem permitted him to go, because 'be'Derech she'Adam Rotzeh Leilech, Molichin Oso' (Makos 10b). Alternatively, brazenness, even towards Hashem, works. Sanhedrin 101a.
Ramban: A sign that he was keen to go and curse Yisrael in keeping with Balak's request.
As indicated by the word "Hu".
The first time, Hashem said 'do not go with them!' It says he went with them, and Hashem was angry (verses 21-22) before he entered Mish'ol ha'Keramim (verse 24)! (PF)
What are the implications of the term "Mal'ach Hashem"?
What is the significance of "the two servants " (Yeinis and Yemris - Targum Yonasan) who accompanied him?
Rashi: An important person does not travel without two servants to accompany him, and they serve each other.
Seforno, Ohr ha'Chayim: Based on the Gemara in B'rachos, 43b, 'When there sare Tthree people, they cannot see the demons but are not harmed by them'. 1
Moshav Zekenim: They were as esteemed as Bil'am (for it says Imo). Regarding Avraham, they were secondary to him (it says Ito. Refer to 22:22:2:11).
And this explains why Bil'am did not see the destructive angel and why he was not harmed by it. However, the angel implied that had the donkey not veered away, he would have killed Bil'am?
What is the significance of "the two servants" (Yeinis and Yemris - Targum Yonasan)?
Rashi: An important person does not travel without two servants to serve him, to ensure that there is always one servant in attendance.
Seforno: Based on the Gemara in B'rachos, 43b 'Three people cannot see the demons but are not harmed by them', it explains why Bil'am did not see the destructive angel (and why he was not harmed by it). 1
See also Or ha'Chayim.
Rashi writes that an important person travels with two servants to serve him, and they serve each other. Since he needs two to serve him, what is the source that they serve each other? In Bereishis (22:3), Rashi explained that he needs two, so when one servant needs to relieve himself, the master will not be left alone!
Bartenura: There, Rashi could not explain that the servants serve each other, for they were Yishmael and Eliezer. Surely R. Yishmael would not serve his father's slave!
Gur Aryeh: Here, there was no concern lest Bil'am be left alone when one servant needs to relieve himself, for they were going with many others. There, Rashi gave a reason why it is forbidden to go with less than two, due to danger, and he said 'one may not go with less than two.' 1
Sifsei Chachamim #1: Regarding Avraham, a Chacham, it is forbidden to go with less than two, due to suspicion when he is alone at night. Here, Rashi teaches why an important person who is not a Chacham should take two.
Sifsei Chachamim #2: Avraham rose early (before dawn), so it was forbidden to take less than two, due to danger, lest be left alone at night. Bil'am did not rise early, so there was no danger. It is proper to take two, so they can serve each other.