Who were the Keini?
Rashi, Ramban and Targum Yonasan: The family of Yisro.
Oznayim (citing Targum Onkelos the Abarbanel and the Malbim): Amon - one of the three additional nations that Hashem promised Avraham Avinu at the B'ris bein ha'Besarim. 1
See Targum Onkelos in Lech-l'cha Bereishis, 15:19 and here.
Why did Bil'am mention the Keini immediately after Amalek?
Rashi and Ramban: Because they lived in Amalek's territory. 1
Da'as Zekenim and Hadar Zekenim: Because whereas Amalek were the first to display hatred towards (or to fight) Yisrael, Keini were the first to show love (or to do Chesed by suggesting the system of judges) for Yisrael. The Torah tells what recompense each one will receive.
Sanhedrin, 107a: Recalling how Yisro and himself had been part of the tribunal 2 in the decree of Par'oh 'Havah Nischakmah lo!', he wondered what his grandchildren were doing sitting among the strongest - on the Sanhedrin. 3
Oznayim la'Torah #1: When Balak told him to flee, he recalled how Yisro had fled from the tribunal of 'Havah Nischakmah lo' 4 , and felt a pang of jealousy when he contrasted Yisro's successful ending to his own downfall. 5
Oznayim la'Torah #2: Refer to 25:2:0.1:2. Because after prophesying about the downfall of Edom and Mo'av - two of the three addional nations that Yisrael are destined to inherit in the time of Mashi'ach, he now prophesies about the downfall of the third nation.
Rashi: As the Pasuk states in Shmuel 1, 15:6. Rashi: And Bil'am wondered how he had merited such greatness - See Divrei Hayamim 1, 2:55.
Sanhedrin (Ibid.): The third member of the tribunal was Iyov; Bil'am, who seconded the decree, was killed, Iyov, who abstained, was stricken with pains, and Yisro who fled merited that his sons sat on the Sanhedrin.
See Torah Temimah citing Sanhedrin (Ibid.), and note 27.
See note on previous answer.
See Oznayim la'Torah.
What are the connotatios of "Eisan Moshavecha"?
Seforno: ?You settled withYisrael in a ?strong? land ? in the desert, a land in which one canoqt plant?.
Sotah, 47b: 'Your dwelling is strong!' - as implied by the continuaton of the Pasuk "ve'Sim ba'Sela Kinecha".
What was Bil'am referring to when he exclaimed "Eisan Moshavecha, ve'Sim be'Sela Kinecha!"?
Rashi: Refer to 24:21:1:1*. And he wondered how Keini merited to dwell in safety together with Yisrael. 1
Ramban: With reference to Pesukim in Shoftim 1:16 ... , he was calling on Yisro to leave his residence among Amalek and to go and live in a safer place 'among the rocks' - with Yisrael, so as not to be destroyed together with Amalek when Yisrael attacked them.
Seforno: With referece to 24:21:1.1:1 - and consequently, you placed 2 your nest in a rock'. 3
Rashbam: 'Do not be disillusioned into thinking that your residence (in Yisrael) is safe and strong, because eventually, Ashur (Sanchreriv) will exile you to a distant land'.
Targum Onkelos: 'Your dwelling is strong and you placed your abode in a strong city'.
Targum Yonasan: 'How strong is your encampment, because you placed your dwelling in a cleft in the rock'.
Oznayim la'Torah: Refer to 24:21:1:5. He was referring to the fact that Amon at this pint were secure, becsuse Yisrael had been commanded to avoid all confrontations with them.
Rashi: Considering that Yisro had sat together with Bil'am in the tribunal that Par'oh convened to decide the fate of Ya'akov's descendents - See Sh'mos, 1:10. Refer to 24:21:1:3**.
Da'as Zekenim and Hadar Zekenim: "Sim" is a noun. The place of your dwelling and nest will be in a rock.
Seforno: With reference to when Yisrael thrived in Eretz Yisrael - in keeping with the adage 'The one who dwelt with you when you were poor will dwell with you when you are rich'.
QUESTIONS ON RASHI
Rashi writes that Yisro and Bil'am were in the tribunal that Par'oh convened to deal with the 'Jewish problem' (Sh'mos 1:10). But the Gemara in Zevachim 116a says that at the time of Matan Torah, the nations asked Bil'am what is happening. It says in Sanhedrin 106b that Bil'am lived only thirty-three years. If so, he must have been born after Matan Torah?
Hadar Zekenim (Sh'mos 1:10, citing R. Menachem of Yuni): The Midrash means that three were in the counsel "L'chah I'atz'cha" 1 (in Pasuk 14), to make Yisrael stumble in Z'nus.
Hadar Zekenim (Sh'mos 1:10, citing R. David): One Midrash says that Bil'am was Lavan's son. He is Bil'am, he is Be'or, he is Lavan 2 (refer to 22:24:1:2 and the notes there), he is Kushan Risha'sayim (a Nochri king in the days of the Shoftim - Sanhedrin 105a). Another Midrash says that he is Ben Nachor 3 , and a third Midrash 4 says that he was Lavan's son. 5 .
Hadar Zekenim: R"M rejects this, since Divrei ha'Yamim of Moshe explicitly says that it was the counsel "Havah Nischachmah Lo" (Sh'mos 1:10). Refer also to 24:21:1:3*.
Da'as Zekenim: According to this, it is fine that the Hagadah says 'Lavan wanted to uproot everything' (totally destroy Yisrael).
Besu'el was Ben Nachor (Bereishis 24:47); Lavan was his grandson. However, we find that Ya'akov called Lavan "Ben Nachor" (Bereishis 29:5)! (PF).
We must say that they are conflicting Midrashim.
We find that Lavan's sons resented Ya'akov (Bereishis). Rashi (Bereishis 31:23,46) says (about Lavan's chase to catch Ya'akov) that Ya'akov's 'brothers' were his sons, and Lavan's 'brothers' were his relatives. If Bil'am was among them, and at the Bris, it is quite appropriate that he was punished for transgressing it! (PF) Hadar Zekenim (in Bereishis 31:52) says that he was Lavan - Lavan's son (Da'as Zekenim ibid. 52) or a descendant of Lavan (Rosh ibid. 48).