Why did Hashem insert the (otherwise superfluous) word "ve'Sha'al Lo ... "?
Yoma, 73a: To teach us that one does not ask the Urim ve'Umim in a loud voice (so that others can hear).,
What are the implications of "Lifnei Hashem"?
Yoma, 73a: Refer to previous answer. It implies that one is obligated to verbalize the question - like Chanah, whose lips moved but who could not be heard by others. 1
Why did Hashem say this to Moshe and not to Yehoshua himself (See Sifsei Chachamim)?
Rashi: In answer to Moshe's request, Hashem is informing him that the Kavod of leadership would not be completely removed from his family, since even Yehoshua would need Elazar. 1
How come that Yehoshua never needed the services of Elazar?
Eruvin, 63a: This was a punishment for Elazar because he Paskened in front of his Rebbe (Moshe) - when he addressed the soldiers who returned from the war against Midyan and taught them the Dinim of Kashering Keilim. 1
See Torah Temimah, note 35.
What decisions is the Torah referring to here?
Rashi: It is referring to going out to war, which required the decision of Elazar via the Urim ve'Tumim and permission from the Sanhedrin. 1
Rashi #2: It is referring to the Urim ve'Tumim. Refer to Shemos, 28:30:4:1:1.
Targum Yonasan: a. Yehoshua will first consult the Urim ve'Tumim via Elazar, who will then announce when to go to war 2 and b. They will come before Yehoshua for litigation. 3
Yerushalmi Sanhedrin 2:5: It i referring to the king consulting the Urim ve'Tumim with regard to a Milchemes ha'Reshus. 4
What are the implications of the term "ke'Mishpat ha'Urim"?
Yoma, 73b: It implies that, although the prediction of a Navi is retractable, 1 that of the Urim ve'Tumim is not. 2
Yerushalmi Shabbos, 2:6: It teaches us that, whenever Yisrael went to war, Beis-Din shel Ma'alah convened to discuss whether they were worthy of success or not. And we learn from here that 'The Satan only prosecutes in time of danger'.
Why does the Torah add the (otherwise superfluous) words end of the Pasuk "Hu ve'Chol B'nei Yisrael ito ve'Chol ha'Eidah"?
Yoma, 73b: In order to Darshen that "Hu", refers to the king, "ve'Chol B'nei Yisrael ito", to the Mashu'ach Milchamah (the Kohrn Gadol for war), and "ve'Chol h'Eidah", to the Sanhedrin - to teach us that one only consults the Urim ve'Tumim on behalf of the king, the Av Beis-Din and someone whom the Tzibur needs. 1
See Torh Temimah, note 41.