The Aleinu prayer is said at the end of each prayer service. It speaks of God as the Supreme King and looks forward to a day when He will be recognized by all nations as the King.
In the Malchuyot section, God is symbolically crowned as King, with His roles as creator of the world and protector highlighted.
עָלֵֽינוּ לְשַׁבֵּֽחַ לַאֲדוֹן הַכֹּל לָתֵת גְּדֻלָּה לְיוֹצֵר בְּרֵאשִׁית שֶׁלֹּא עָשָֽׂנוּ כְּגוֹיֵי הָאֲרָצוֹת וְלֹא שָׂמָֽנוּ כְּמִשְׁפְּחוֹת הָאֲדָמָה שֶׁלֹּא שָׂם חֶלְקֵֽנוּ כָּהֶם וְגוֹרָלֵֽנוּ כְּכָל הֲמוֹנָם: שֶׁהֵם מִשְׁתַּחֲוִים לַהֶֽבֶל וָרִיק וּמִתְפַּלְּלִים אֶל אֵל לֹא יושִֽׁיעַ. וַאֲנַֽחְנוּ כֹּרְעִים וּמִשְׁתַּחֲוִים וּמוֹדִים לִפְנֵי מֶֽלֶךְ מַלְכֵי הַמְּלָכִים הַקָּדוֹשׁ בָּרוּךְ הוּא. שֶׁהוּא נוֹטֶה שָׁמַֽיִם וְיוֹסֵד אָֽרֶץ. וּמוֹשַׁב יְקָרוֹ בַּשָּׁמַֽיִם מִמַּֽעַל. וּשְׁכִינַת עֻזּוֹ בְּגָבְהֵי מְרוֹמִים. הוּא אֱלֹהֵֽינוּ אֵין עוֹד. אֱמֶת מַלְכֵּֽנוּ אֶֽפֶס זוּלָתוֹ כַּכָּתוּב בְּתוֹרָתוֹ וְיָדַעְתָּ הַיּוֹם וַהֲשֵׁבֹתָ אֶל לְבָבֶֽךָ כִּי יְהֹוָה הוּא הָאֱלֹהִים בַּשָּׁמַֽיִם מִמַּֽעַל וְעַל הָאָֽרֶץ מִתָּֽחַת אֵין עוֹד:
It is our obligation to praise the Master of all, to ascribe greatness to the Creator of [the world in] the beginning: that He has not made us like the nations of the lands, and has not positioned us like the families of the earth; that He has not assigned our portion like theirs, nor our lot like that of all their multitudes. For they prostrate themselves to vanity and nothingness, and pray to a god that cannot deliver. But we bow, prostrate ourselves, and offer thanks before the Supreme King of kings, the Holy One blessed is He, Who spreads the heavens, and establishes the earth, and the seat of His glory is in the heaven above, and the abode of His invincible might is in the loftier heights. He is our God, there is nothing else. Our King is true, all else is insignificant, as it is written in His Torah: “And You shall know this day and take into your heart that Adonoy is God in the heavens above and upon the earth below; there is nothing else.”
Clue #4
The Zichronot (Remembrance) section lists many events that God remembers. Go to the first paragraph of Zichronot. Which person - who is not one of the forefathers - is mentioned? Once you have discovered the person, find the verse in Genesis that mentions him and his animals. (Sefaria tip: Click on the Zichronot paragraph to open the resource panel. Click on "Tanakh" to find the direct link to the verse.) What other events are mentioned among the remembrances? Why do you think that we want God to remember those events on Rosh Hashanah?
Clue #5 will be found in "sheets" for the Genesis verse.