Why does this blessing say God redeemed us, when I am about to ask for help?
The blessing ends with ga'al Yisrael, "who redeemed Israel." That is the past tense. A moment later you stand for the Amidah and ask for what you still need. It looks like the wrong order.
The Mishnah Berurah (a central commentary on daily Jewish law, written around 1900) says the past tense is on purpose. This blessing is about the Exodus from Egypt, so it speaks about what already happened. The seventh blessing of the Amidah ends goel Yisrael, "Redeemer of Israel," and there the wording changes because that is where we ask, and we are asking about what is still ahead.
The Mishnah (the first written collection of Jewish oral law, about 1,800 years old) shows the same two words closing a blessing that looks forward. At the Pesach Seder, Rabbi Akiva's blessing after Hallel asks God to bring us to future holidays in peace, happy in the rebuilding of Jerusalem. It still ends, "Blessed are You, Hashem, who redeemed Israel."
Now look at the lines just before the ending. "Rock of Israel, arise to the help of Israel, and redeem Judah and Israel as You promised" is a request about the future. Abudarham notices a difference between morning and night. In the morning the next line says "Our Redeemer," because by day we are asking Him to redeem us. At night the prayer uses another verse, "For Hashem redeemed Yaakov and saved him from a hand stronger than his," because by then He has already saved us.
So the order is on purpose: first what God already did, then what you still need.
Mishnah Berurah 66:33,Mishnah Pesachim 10:6,Abudarham, Blessings on the Shema,Yirmeyahu 31:11Does "who is like You among the mighty" mean there are other gods?
In Hebrew the word is elim, and it looks like the word for gods. If God is being compared to them, it can sound as if they exist.
The classic commentators answer in a few ways. Rashi says elim here just means "the mighty," the way Yechezkel 17:13 calls the strong men of a land eilei ha'aretz. The Ramban (Rabbi Moshe ben Nachman, Spain, 1200s) agrees the word means strength, but says this verse is about angels, who are also called elim, the way Devarim 10:17 calls God "God of gods." Ibn Ezra also says angels.
The old Aramaic translation of the Torah, Targum Onkelos, turns the question into a statement: "There is none besides You, for You are God, Hashem."
The Mekhilta lists several readings side by side. Who is like You among those who serve You above. Among rulers who called themselves gods: Pharaoh, who said of the Nile, "The Nile is mine, and I made myself" (Yechezkel 29:3), and also Sancherev and Nebuchadnezzar. Among idols that "have a mouth but cannot speak" (Tehillim 115:5). In the last two readings the so-called gods are only claims, not real rivals.
The Mekhilta adds that when the nations heard that Egypt had fallen, they dropped their idols and said these same words. Another reading, "who is like You among the silent," is in the Az Yashir unit. The commentators disagree about who the elim are. None of the readings above says that another god exists.
Rashi, Ramban and Ibn Ezra on Shemot 15:11,Targum Onkelos on Shemot 15:11,Mekhilta DeRabbi Yishmael, Shirah 8,Yechezkel 17:13 and 29:3,Devarim 10:17Why does the prayer say the people sang a "new song" at the sea? New compared to what?
The line says the redeemed praised God at the shore with shirah chadashah, "a new song." What makes it new? Abudarham ties the words to Tehillim 40:4, "He put a new song in my mouth." The verses just before it describe being lifted out of a muddy pit. And at the Seder, he notes, we say "we will thank You with a new song for our redemption." Both link a new song to being rescued.
Then he asks about the grammar. Shirah is feminine. The verse about the future uses shir, which is masculine: "Sing to Hashem a new song" (Tehillim 98:1). He gives two reasons. The first comes from a Midrash on Shir HaShirim: a daughter received a tenth of her father's property, and Israel took a land that was a tenth of the lands of the nations. In the future Israel will inherit like a son, who gets everything, and then the song will be masculine.
His second reason comes from the Mekhilta, an early Midrash on Shemot, and Shemot Rabbah says it too. All the songs so far are feminine, like a woman who gives birth and then gives birth again. Each rescue was followed by new slavery, and Shemot Rabbah names Babylon, Media, Greece and Edom. But in the future there will be no more troubles, as Yeshayahu 65:16 says: "the earlier troubles are forgotten." Then the song will be masculine.
So in these sources a new song goes with being rescued. The song at the sea is feminine because it was not the last one. The masculine song, with nothing bad after it, is still ahead.
That fits what comes next in the prayer. After the song, we ask: "Rock of Israel, arise to the help of Israel."
Abudarham, Blessings on the Shema,Mekhilta DeRabbi Yishmael, Shirah 1,Shemot Rabbah 23:11,Tehillim 40:2-4 and 98:1,Yeshayahu 65:16