Why will the mountains drip juice?
Radak: After the nations are eradicated, there will be great good for Yisrael. A Mashal for it is that they will receive good without toil.
Malbim: The influence and Brachah will be so great that mountains will drip with juice due to the many sweet fruits.
What is the significance of "veha'Geva'os Telachnah Chalav"?
Radak: Due to the great flowing and spilling, the going (flow) is called hills, even though it is the milk that goes. It similarly says that the Afikim will go, even though really the water goes. We find also "va'Teradnah 1 Eineinu Dim'ah" (Yirmeyah 9:17).
Malbim: This is due to the abundance of cattle and flock.
This is Po'el Omed; the action applies to the subject, i.e. the eyes themselves descend. (PF)
What are "Afikei"?
Rashi: It is a source of water.
Radak: They are valleys in which water flows.
Will a spring come out of Beis Hashem?
Radak: Yes, like it says in Yechezkel (47:1). Malbim - it is also in Zecharyah (13:1). Until now, there was a shortage of water in Eretz Yisrael in general, and in Yerushalayim in particular; there were no springs there 1 . In the future, not only will there be water in Yehudah - a spring will come out of Beis Hashem and water the valley of Shitim.
Malbim: This hints to Torah and Emunah, which are compared to water, emerging from Beis Hashem to the entire world.
Yuma 31a: Ein Eitam was higher than the Azarah; from it came the channel that brought water to where Kohanim immersed (Rashi 31a)! An Amah of water flowed through the Mikdash (Yuma 44b)! Malbim's words require investigation. (PF)
Why does it say "v'Hishkah Es Nachal ha'Shitim"?
Rashi citing Targum Yonasan: It will water the valley of Shitim. Radak - a valley is called Nachal whether or not it has water, e.g. "va'Yachperu Avdei Yitzchak ba'Nachal" (Bereishis 26:19). Chazal said, [how can] a city [be close to a walled city, but not seen from it? It] is in a Nachal (Megilah 3b).
Rashi, from Tanchuma Balak 17: It will atone for the sin of [Ba'al] Pe'or [in Shitim]. Malbim - in Shitim, Yisrael breached with Zenus and idolatry; it was the first sin for Yisrael 1 . The Kadosh spring will be Metaher the Tum'ah that began in Nachal ha'Shitim, and it will remove the foreign evils and desires.
Radak citing Rav Sadya Gaon: Nachal ha'Shitim is the Yarden, for it is close to the place called Shitim.
The Meraglim was Yisrael's 10th sin (Bamidbar 14:22)! Perhaps Malbim means the first sin of idolatry; Chet ha'Egel does not count, for 'Yisrael were not worthy to sin.' [Hashem pushed them into it, to show that Teshuvah can help for the Tzibur, even for such a great sin] (Avodah Zarah 4b). (PF)