1) "YEHEI SHEMEI RABA MEVORACH..."
QUESTION: The Gemara relates that Eliyahu ha'Navi told Rebbi Yosi that whenever Jews enter the synagogues and study halls and respond, "Yehei Shemei ha'Gadol Mevorach..." -- "May His great Name be blessed...," the Holy One, blessed is He, says, "Happy is the King whose people praise Him in His house like this, and woe to the sons who were exiled from the table of their Father."
RASHI (DH Ashrei ha'Melech) says that Hash-m was declaring how happy He was when His people praised Him "with this praise inside the Beis ha'Mikdash." When, though, was the praise of "Yehei Shemei" ever recited in the Beis ha'Mikdash?
ANSWER: The Gemara in Pesachim (56a) says that when Yakov Avinu blessed his sons before he died, he announced, "Baruch Shem Kevod Malchuso l'Olam Va'ed!" -- "Blessed be the Name of His glorious kingdom for all eternity!" The Targum Yerushalmi (to Bereishis 49:2), however, says that Yakov declared, "Yehei Shemei Raba...."
This discrepancy can be explained as follows. The Gemara in Pesachim (which relates the story in Hebrew, and not in Aramaic) quotes the Hebrew version of Yakov's reply -- "Baruch Shem Kevod Malchuso l'Olam Va'ed." The Targum, though, relates the story in Aramaic. Perhaps "Yehei Shemei Raba..." ("May His great Name be blessed for all eternity!") is simply an Aramaic rendering of the Hebrew "Baruch Shem..." ("Blessed be the Name of His glorious kingdom for all eternity!"). (The slight difference between the two is not problematic. The Targum, an Aramaic rendering, is not meant to be a literal translation, but rather is meant to convey the idea contained in the Hebrew phrase. See Kidushin 49a and Tosfos there.)
Since the Jews used to declare "Baruch Shem..." in the Beis ha'Mikdash every day (it was said in place of "Amen"; see Ta'anis 16b, cited by Rashi to Berachos 54a, DH Kol Chosmei Berachos), they indeed were saying "Yehei Shemei Raba..." in its Hebrew form! That is what Rashi means when he says that they used to praise Hash-m "with this praise inside the Beis ha'Mikdash."
This idea also answers a question that Tosfos asks. Tosfos gives two explanations for the recitation of "Yehei Shemei Raba" in Aramaic. The first explanation that Tosfos cites is what he refers to as the "common explanation." Some assert that the Kaddish prayer was written in Aramaic due to its unusual holiness. Were we to recite it in Hebrew, it might arouse the jealousy of the angels in heaven! We therefore say this praise in Aramaic, a language which the angels do not recognize (Shabbos 12b).
Tosfos does not accept this explanation. He argues that we say many beautiful prayers which are in Hebrew, and we are not concerned with arousing the jealousy of the angels. Why should this prayer arouse the angels' jealousy more than any other?
The answer to this question may be as follows. The Midrash (Devarim Rabah 2:25) relates that Moshe Rabeinu "stole" the praise "Baruch Shem..." from the angels when he heard it from them while he was in heaven receiving the Torah. We, therefore, "hide" it from the angels by saying it in a whisper.
Perhaps this is why we want to "hide" the Kaddish prayer from the angels' ears. As we noted, "Yehei Shemei Raba" is an Aramaic rendering of "Baruch Shem" -- the praise that Moshe Rabeinu "stole" from the angels. Perhaps it is for this reason that "Yehei Shemei Raba" must be recited in Aramaic, the language that the angels do not recognize. (This answer to Tosfos' question is suggested in SEFER V'IMRU AMEN by Rav Yehoshua Alter Wildman, Jerusalem, 1929, 2:59, pp. 90-91, in the name of Rav Menachem Mordechai Frenkel of Jerusalem.)