1) ALL AGREE THAT THE TORAH WAS GIVEN ON SHABBOS
AGADAH: The Gemara explains that while the day of the month on which the Torah was given may be subject to dispute, everyone agrees that the Torah was given on Shabbos.
What is the significance of the fact that the Torah was given on Shabbos?
Shabbos is the day dedicated to the pursuit and achievement of holiness and purity through the study of Torah and the Mitzvos. We find this theme in a number of places. David ha'Melech declares, "How I love Your Torah, it is my speech all of the day" (Tehilim 119:97). The words that he uses are not, "It is my speech all day," but rather, "it is my speech all the day." "The day" refers to the unique day, the day of Shabbos. On Shabbos, David ha'Melech would dedicate himself completely to the joy of the study of the Torah. (See RABEINU BACHYE, Shemos 20:8.)
Similarly, there is only one section of the Torah that begins with the convening of an assembly. At the beginning of Parshas Vayakhel, the Torah relates that "Moshe assembled the Jewish people," and it continues with the commandment to observe the Shabbos. The Midrash relates that Hash-m told Moshe, "Make large assemblies [on Shabbos] and expound the laws of Shabbos publicly before the people, in order that future generations will learn from you to do the same" (Yalkut Shimoni #408).
We also find this theme in the Midrash that relates that the Torah complained before Hash-m and said, "When the Jewish people enter Eretz Yisrael, everyone will become preoccupied with their agricultural pursuits; what will become of me then?" Hash-m answered, "I have an excellent partner for you: the Shabbos. On that day, the Jews are not busy with their work, and they will be free to occupy themselves in the study of Torah." (TUR OC 290; see also Tana D'vei Eliyahu Rabah, ch. 1). (For more on this subject, see Rabbi Mordecai Kornfeld's "Torah from the Internet," Parshas Vayakhel.)