Why did Bil'am mention the Keini (Yisro) immediately after Amalek?
Rashi and Ramban: Because they lived close to Amalek. 1
Da'as Zekenim, Hadar Zekenim: Amalek were the first to show hatred for (or fight) Yisrael, and Keini were the first to show love (or do Chesed, i.e. suggest the system of judges) for Yisrael. The Torah tells what recompense each will get!
What was Bil'am referring to when he exclaimed "Eisan Moshavecha, ve'Sim be'Sela Kinecha!"?
Ramban: With reference to Pesukim in Shoftim 1:16 ... , he was calling on him 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.
Rashbam: 'Don't 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: 'When he saw how Yisro had converted, he exclaimed - "How strong is your encampment, because you placed your dwelling in a cleft in the rock" '.
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.
Seforno: With reference to Yisrael in the desert
Da'as Zekenim, 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'.
Rashi writes that Yisro and Bil'am were in the tribunal that Pharaoh convened to deal with the 'Jewish problem' (Shemos 1:10). 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 33 years. If so, he was born after Matan Torah!
Hadar Zekenim (Shemos 1:10, citing R. Menachem of Yuni): The Midrash means that three were in the counsel "Lechah I'atzecha" 1 (verse 14), to make Yisrael stumble in Zenus. (This answers the question from the counsel, but not from Matan Torah.)
Hadar Zekenim (Shemos 1:10, citing R. David): A 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 another Midrash says that he was Lavan's son. 4 We must say that the Midrashim argue.
Hadar Zekenim: R"M rejected this, for Divrei ha'Yamim of Moshe explicitly says that it was the counsel "Havah Nischachmah Lo" (Shemos 1:10)!
Da'as Zekenim: According to this, it is fine that the Hagadah says 'Lavan wanted to uproot everything' (totally destroy Yisrael).
We find that Lavan's sons resented Yakov (Bereishis). Rashi (Bereishis 31:23,46) says (about Lavan's chase to catch Yakov) that Yakov'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 (Bereishis 31:52) says that he was Lavan, i.e. Lavan's son (Da'as Zekenim ibid. 52) or a descendant of Lavan (Rosh ibid. 48).