Why did Moshe say to the people "Re'u!"? What were they supposed to see?
Rashi: The fact that a double portion of Manna fell on Friday served as visual evidence that Hashem had sanctified the Shabbos and that they were not supposed to collect Manna on it.
Seforno: "Re'u" means (not See, but) Reflect - that Shabbos is not just a Mitzvah, but a unique gift that Hashem gave to you exclusively. 1
As the Gemara states in Shabbos (6b), and as we say in the Amidah 'And He did not give it to the nations of the world', and we continue 'And Bnei Yisrael will keep the Shabbos, to make the Shabbos for all generations - in order to attain a day that is all Shabbos (Olam ha'Ba [Seforno])'.
What did Moshe mean when he said "Sh'vu Ish Tachtav"?
Rashi #1: This hints at the Din de'Rabbanan prohibiting someone who travels outside the T'chum Shabbos to walk four Amos from his destination. 1
Targum Yonasan: He is teaching the prohibition of carrying from one major domain to the other and of carrying four Amos in the public street. 2
What did he mean when he said "Al Yeitzei Ish mi'Mekomo be'Yom ha'Shabbos"?
Rashi #1: It hints at the Din de'Rabbanan prohibiting traveling beyond the T'chum of two thousand Amos on Shabbos. 1
Rashi #2: Basically, Moshe was ordering them to remain in the camp and not to go out to collect the Manna on Shabbos.
Rashi on the Beraisa of R. Yishmael cites this as an example of 'Davar ha'Lameid mi'Inyano'. Seeing as the Parshah is talking about the Manna, which they had to travel two thousand Amos to collect, the Pasuk must be issuing a prohibition against traveling more than two thousand Amos on Shabbos, and not against moving from one's current location of four Amos.
Why does it say that Hashem gave to you Shabbos (in the past tense)?
Moshav Zekenim (5:4): When Moshe was in Pharaoh's house, Moshe convinced him that slaves will work better if they have a day of rest. Pharaoh let Yisrael choose a day, Hashem caused them to pick Shabbos. 1