What is the meaning of the first half of the Pasuk?
Rashi (citing Targum Onkelos): It means 'Water will flow from their wells', with reference to a king that will arise from their ranks who will rule over many nations. 1
Targum Yonasan: It means that their kings and their redeemers will come from their own ranks, and their children, the sons of Ya'akov will rule over many nations.
Refer to 24:5:1:3*.
Da'as Zekenim and Hadar Zekenim (on Pasuk 1): It means 'Water will drip from its source' - with reference to legions that will increase greatly from his seed. 2
Nedarim, 81a: Based on the fact that ?Mayim? generally refers to Torah, and 'Dal' means a poor person, it can mean 'Watch the poor, because from them Torah will emerge!' 3
Oznayim la'Torah #1: It means that - in spite of the natural scarcity of water in Eretz Yisrael, water will be in such abundance that it will 'spill over from the buckets' and when the planting season arrives, 'there is an abundance of water for the seeds'.
Oznayim la'Torah #2: It means that Torah will flow from Yisrael's wellsprings, and the nations of the world (although they did not accept the Torah) will drink from it - they will draw from it many of its logical Mitzvos - such as Kibud Av va'Eim and the prohibition against murder and theft. 4
Rashi: He will succeed - like a seed that is planted in water. See also Ba'al ha'Turim, who comments that one only anoints a king by a river.
Da'as Zekenim and Hadar Zekenim (Ibid.): Because legions are compared to water ? as in Yeshayah 8:7 "Mei ha'Nahar? Melech Ashur".
See Torah Tem imah, note 15.
See Oznayim la'Torah, who elaborates.
To whom is ve'Yarom me'Agag "Malko" referring?
Rashi and Targum Yonasan: It refers to Shaul ha'Melech - their first king, who will capture Agag, king of Amalek.
How could Bil'am name the king of Amalek before he was born?
Ramban #1 (citing Rashi): Indeed, Bil'am is pre-naming Agag before he was born. 1
Ramban #2, Rashbam, Da'as Zekenim and Hadar Zekenim (in Pasuk 1): All kings of Amalek were called Agag. 2
Ramban (Ibid.): Just as we find by Koresh, king of Persia - in Yeshayah (45:1), by Yoshiyahu, king of Yehudah - in Melachim 1, 13:2, by Yitzchak and Yishmael - in Bereishis 17:19 & 16:11, respectively and by Shlomoh ha'Melech - in Divrei ha'Yamim 1, 22:9. See Ramban, as to why he opts for his second explanation.
Rashbam: Just as all the kings of Egypt were called Par'oh; all the kings of P'lishtim, Avimelech and all the kings of Yerushalayim, Malki-Tzedek.
What are the implications of "ve'Sinasei Malchuso"?
Rashi and Ramban,: It implies that the kngdom of Ya'akov will go from strength to strength, because David and Shlomoh will follow.
Targum Yonasan: It implies that he (king Shaul) will rise over Agag their king. 1
Refer to 24:5:1:6*.
Targum Yonasan: But because he will have compassion on Agag, his kingdom will be taken away from him.
Why has Bil'am switched to the future tense "Yizal", "Yarom", "Sinasei"?
Because he is now hinting at the future evolving of Yisrael and of the other nations.