What are the implications of "Vaya'avru be'Soch ha'Yam ha'Midbarah"?
Targum Yonasan: This strange contradictory Lashon teaches us that Yisrael were busy as they crossed the Yam-Suf collectring gems and pearls. 1
Oznayim la'Torah: After Yisrael witnessed the miracles that Hashem performed with them in the Sea, they were not afraid to follow Him in the desert.
See Peirush Yonasan and Na'ar Yonasan.
The Torah mentions the three days journey until Marah, the springs and date trees in Eilim. Why does it not mention Matan Torah or Korach's rebellion?
Elef ha'Magen: Because, when the Torah wrote - in Pasuk #1 - that Hashem took them out "be'Yad Moshe ve'Aharon" "be'Yad Moshe" means on the merit of Torah and "Aharon", on the merit of Avodah - hinting broadly at Matan Torah and the episode of Korqach.
What is the significance of the three days until they came to Marah?
Elef ha'Magen: Refer to 33:8:151:1. In Sh'mos 5:22 it says they were three days without water - Torah (Bava Kama 82a). Therefore, they received some Mitzvos at Marah. In Mitzrayim, they did not realize they are lacking Torah; now they began to thirst for Torah.