1. "There (at Marah) did He provide for it (Israel) Law and there did He test it." (Shmos 15:25). Our sages explain (Sanhedrin 56b) that the "Law" refers to the regulations of Shabbos, establishment of a court system and honoring one's parents. What do these laws have in common? Why did Hashem dictate them at Marah?
The story of Marah is very strange, indeed. The Jews had just crossed the Sea of Reeds three days beforehand, and - suddenly - they took to complaining about the bitter ("mar") water. Why did they act in such a manner?
It may very well be that Bnei Yisroel responded with complaints as a reflection of their slavery experience. The Jews - who were just emancipated - did not previously have responsibility for themselves, to a large degree, and they thus reacted to the bitter water with gripes, for this is the way of slaves, who do not have a sense of security about their well-being and lack social and legal structures within which to work for remedies to problems. Thus, Hashem provided laws which addressed these needs. Shabbos represents the ultimate authority of God as creator and controller of all. God is the caretaker par excellence, and Bnei Yisroel needed to understand that they were in His secure hands. The court system reflects the legal structure, vesting authority in the sages to rule and mediate. Honoring one's parents provides a structure of authority within the family. It was essential for the Jews to learn that they were always in God's hands, and a proper sense of authority had to be taught. It may be for this reason that the same bitter waters were rendered sweet and potable (rather than new water being provided), for the Jews' shortcoming was in attitude, not in substance, and a change in attitude to reliance on God and proper acceptance of the authority of Moshe were all that was needed.
2. "And Miriam the prophetess, Aharon's sister, took the drum in her hand, and all of the women went out after her...And Miriam answered them, 'I shall sing to God for He is exalted; horse and chariot has He heaved in the sea.'" (16:20-21) Why are Miriam's credentials recounted? Must we really know that she was Aharon's sister and a prophetess in her own right?
Perhaps the Torah is teaching at this juncture that one cannot be innovative or creative in halacha or minhag without credentials or precedent. Miriam's initiation of a women's song could have been viewed as innovative and daring, and - lacking her credentials - her move would likely have not been tolerated or sanctioned by Mesorah (Tradition).
3. The haftarah for the seventh day of Pesach consists of Dovid's song of thanksgiving to Hashem for salvation from his enemies. This haftarah parallel's the Torah reading of the day, which features the Song at the Sea, which is Israel's thanks for God's miracles at that site. Why, then, do we read a different haftarah on Parshas Beshalach - namely, that of Hashem's salvation of the Jews at the time of Devorah, which is comprised of both narrative and song?
The theme of Beshalach is that of faith in God. Nachshon entered the sea while it was yet wet, trusting that God would split the waters. The Medrash explains that Jews attained purity of faith once they passed through the sea, as it says upon their passage, "...and they believed in Hashem and in Moshe, His servant." (See Haggadas Siach Ha'Grid.) Bnei Yisroel were punished at the end of the parshah with the arrival of Amalek, which symbolizes lack of belief in God, when the Jews failed in their faith at Rephidim. (17:1, 8 with Rashi from Medrash.) (In fact, one of the parsha's simanim is "emunah".) The theme of the story of Devorah is precisely one of faith against all odds. Devorah charged Barak with attacking Sisera, per God's command, even though the logistics were on the enemy's side. Her song of thanks was a burst of emunah in Hashem's salvation; this is the exact correlation with Parshas Beshalach which warrants the reading of Shiras Devorah as the haftarah.