Hebrew, then English. Open "What it means" under any line for the explanation.
Kedushah DeSidra continues. A verse from Divrei HaYamim (Chronicles) I 29:18:
יְיָ אֱלֺהֵי אַבְרָהָם יִצְחָק וְיִשְׂרָאֵל אֲבוֹתֵינוּ שָׁמְרָה זֹאת לְעֹלָם לְיֵצֶר מַחְשְׁבוֹת לְבַב עַמֶּךָ וְהָכֵן לְבָבָם אֵלֶיךָ.
Hashem, God of Avraham, Yitzchak and Yisrael, our fathers keep this forever as the shaping of the thoughts of Your people's hearts and set their hearts firmly toward You
What it means
Hashem, God of Avraham, Yitzchak and Yisrael, our fathers: keep this forever, to shape the thoughts of Your people's hearts, and set their hearts firmly toward You.
In Chronicles, David says this after the people gave freely to build the Temple. The commentary printed under the name of Rashi (the classic commentator, France, died 1105) says "this" is that gift. Abudarham (a commentary on the prayers, Spain, around 1340) says that here it asks that this Kedushah shape our thoughts and aim our hearts at God.
Divrei HaYamim I 29:18 (commentary printed as Rashi's); Abudarham, Post Amidah 26From Tehillim (Psalms) 78:38:
וְהוּא רַחוּם יְכַפֵּר עָוֹן וְלֺא יַשְׁחִית וְהִרְבָּה לְהָשִׁיב אַפּוֹ וְלֺא יָעִיר כָּל חֲמָתוֹ.
And He, the merciful One, forgives wrongdoing and does not destroy and again and again turns back His anger and does not stir up all His rage
What it means
And He, the merciful One, forgives wrongdoing and does not destroy. Again and again He turns back His anger and does not stir up all His rage.
This verse also opens Vehu Rachum, the long prayer of pleading added on Mondays and Thursdays, and the Romemu page tells its story. Look at the verse just before it: in Tehillim 78:37, that generation's heart "was not firm" with God. "Firm" there is the same root as "set firm" in the line above. God forgives anyway.
Tehillim 78:37-38; Divrei HaYamim I 29:18From Tehillim 86:5:
כִּי אַתָּה אֲדֹנָי טוֹב וְסַלָּח וְרַב חֶסֶד לְכָל קֹרְאֶיךָ.
For You, my Master, are good and forgiving and great in kindness to all who call to You
What it means
Radak (Rabbi David Kimchi, Provence, around 1200) says "good" means good to every creature, as in "Hashem is good to all" (Tehillim 145:9). "Forgiving" is for those who sin. Ibn Ezra (a Spanish commentator who died in the 1160s) says: good to the good, and forgiving to sinners.
Radak and Ibn Ezra on Tehillim 86:5From Tehillim 119:142:
צִדְקָתְךָ צֶדֶק לְעוֹלָם וְתוֹרָתְךָ אֱמֶת.
Your righteousness is justice forever and Your Torah is truth
What it means
Radak says "Your Torah is truth" means two things. All its mitzvot are true, and the promises it makes to those who keep it are true and will not turn out false.
Radak on Tehillim 119:142From Michah (Micah) 7:20:
תִּתֵּן אֱמֶת לְיַעֲקֹב חֶסֶד לְאַבְרָהָם אֲשֶׁר נִשְׁבַּעְתָּ לַאֲבוֹתֵינוּ מִימֵי קֶדֶם.
You will give truth to Yaakov kindness to Avraham which You swore to our fathers from long ago
What it means
You will give truth to Yaakov and kindness to Avraham, which You swore to our fathers in days of old.
Rashi (the classic commentator, France, died 1105) reads this as God keeping His promises. The "truth" is what He promised Yaakov. The "kindness" is the reward for Avraham's kindness. And the oath, he says, was made at the binding of Yitzchak.
Rashi on Michah 7:20From Tehillim 68:20:
בָּרוּךְ אֲדֹנָי יוֹם יוֹם יַעֲמָס לָנוּ הָאֵל יְשׁוּעָתֵנוּ סֶלָה.
Blessed is my Master day after day He loads us with blessing the God who is our rescue Selah
What it means
The Gemara (the rabbis' discussions built on the Mishnah, the first written collection of their teachings) tells of two sages. Shammai the Elder saved the finest animal he found all week for Shabbat. Hillel the Elder had a different way, and the Gemara points to this verse. Rashi says Hillel trusted that a fine animal would come his way for Shabbat.
Beitzah 16a, with RashiFrom Tehillim 46:8:
יְיָ צְבָאוֹת עִמָּנוּ מִשְׂגָּב לָנוּ אֱלֺהֵי יַעֲקֹב סֶלָה.
Hashem of hosts is with us a stronghold for us is the God of Yaakov Selah
What it means
Hashem of hosts is with us. The God of Yaakov is a stronghold for us. Selah.
These three verses, in this order, are also said at Havdalah, the ceremony that ends Shabbat (Siddur Sefard). The Pitum HaKetoret and Romemu pages tell what the Yerushalmi (the Gemara of the Land of Israel) says about the first two.
Siddur Sefard, Havdalah; Yerushalmi, Berakhot 5:1From Tehillim 84:13:
יְיָ צְבָאוֹת אַשְׁרֵי אָדָם בֹּטֵחַ בָּךְ.
Hashem of hosts, happy is the person who trusts in You
From Tehillim 20:10:
יְיָ הוֹשִׁיעָה הַמֶּלֶךְ יַעֲנֵנוּ בְיוֹם קָרְאֵנוּ.
Hashem, save us may the King answer us on the day we call
Not a verse. A prayer built from pieces of verses and the sages' own words:
בָּרוּךְ הוּא אֱלֺהֵינוּ שֶׁבְּרָאָנוּ לִכְבוֹדוֹ וְהִבְדִּילָנוּ מִן הַתּוֹעִים
Blessed is He, our God who created us for His glory and set us apart from those who go astray
What it means
Abudarham says this line is built from verses. "Created us for His glory" comes from Yeshayahu (Isaiah) 43:7, and he explains glory here as praising Him. "Set us apart" comes from Vayikra (Leviticus) 20:26, where God says, "I set you apart from the peoples to be Mine."
Abudarham, Weekday Prayers, Post Amidah 27-28; Yeshayahu 43:7; Vayikra 20:26וְנָתַן לָנוּ תּוֹרַת אֱמֶת וְחַיֵּי עוֹלָם נָטַע בְּתוֹכֵנוּ
and gave us the Torah of truth and eternal life He planted within us
What it means
and gave us the Torah of truth, and planted eternal life within us.
Abudarham traces "Torah of truth" to Tehillim 119:142, which you said above. The blessing after a Torah reading uses the same words, and the page for that blessing explains "planted."
Abudarham, Weekday Prayers, Post Amidah 29; Tehillim 119:142הוּא יִפְתַּח לִבֵּנוּ בְּתוֹרָתוֹ וְיָשֵׂם בְּלִבֵּנוּ אַהֲבָתוֹ וְיִרְאָתוֹ
May He open our heart to His Torah and put in our heart love of Him and awe of Him
What it means
May He open our heart to His Torah, and put love of Him and awe of Him in our heart.
וְלַעֲשׂוֹת רְצוֹנוֹ וּלְעָבְדוֹ בְּלֵבָב שָׁלֵם לְמַעַן לֺא נִיגַע לָרִיק וְלֺא נֵלֵד לַבֶּהָלָה.
and to do His will and to serve Him with a whole heart so that we will not toil for nothing and not give birth for terror
What it means
and to do His will and serve Him with a whole heart, so that we will not toil for nothing and not give birth for terror.
Abudarham says the ending comes from Yeshayahu 65:23. There it is a promise about a blessed future, and Radak says "not give birth for terror" means parents will not see their children die. Here the siddur makes it first person: "we."
Abudarham, Weekday Prayers, Post Amidah 31; Yeshayahu 65:23, with RadakAnother prayer, not a verse:
יְהִי רָצוֹן מִלְּפָנֶיךָ יְיָ אֱלֺהֵינוּ וֵאלֺהֵי אֲבוֹתֵינוּ שֶׁנִּשְׁמֹר חֻקֶּיךָ בָּעוֹלָם הַזֶּה וְנִזְכֶּה וְנִחְיֶה וְנִרְאֶה וְנִירַשׁ טוֹבָה וּבְרָכָה לִשְׁנֵי יְמוֹת הַמָּשִׁיחַ וּלְחַיֵּי הָעוֹלָם הַבָּא.
May it be Your will, Hashem our God and God of our fathers, that we keep Your laws in this world and be worthy to live, to see, and to inherit goodness and blessing in the days of the Messiah and in the life of the World to Come
What it means
Abudarham says "keep Your laws in this world" comes from Tehillim 119:5: "If only my ways were set firm to keep Your laws." He says why "this world": it is the world of action, and through action we earn the goodness and blessing of the World to Come.
Abudarham, Weekday Prayers, Post Amidah 32; Tehillim 119:5From Tehillim 30:13, the end of Mizmor Shir:
לְמַעַן יְזַמֶּרְךָ כָבוֹד וְלֺא יִדֹּם יְיָ אֱלֺהַי לְעוֹלָם אוֹדֶךָּ.
so that my soul will sing to You and not go silent Hashem, my God, I will thank You forever
What it means
The Hebrew says "so that glory will sing to You." Radak says glory here means the soul, and he ties it to David's question a few verses earlier, "Will dust thank You?" The Mizmor Shir page has the whole discussion.
Radak on Tehillim 30:13From Yirmiyahu (Jeremiah) 17:7:
בָּרוּךְ הַגֶּבֶר אֲשֶׁר יִבְטַח בַּייָ וְהָיָה יְיָ מִבְטַחוֹ.
Blessed is the person who trusts in Hashem and Hashem is their security
What it means
The verse before this one in Yirmiyahu is the opposite: "Cursed is the man who trusts in people." After this one comes a picture of the trusting person as a tree by water that does not worry in a dry year. The Halleluyah 146 page asks if this rules out relying on people.
Yirmiyahu 17:5-8From Yeshayahu (Isaiah) 26:4:
בִּטְחוּ בַייָ עֲדֵי עַד כִּי בְּיָהּ יְיָ צוּר עוֹלָמִים.
Trust in Hashem forever for in Yah Hashem is the Rock of the ages
From Tehillim 9:11:
וְיִבְטְחוּ בְךָ יוֹדְעֵי שְׁמֶךָ כִּי לֺא עָזַבְתָּ דֹרְשֶׁיךָ יְיָ.
And they will trust in You those who know Your Name for You have not abandoned those who seek You, Hashem
What it means
And those who know Your Name will trust in You, for You have not abandoned those who seek You, Hashem.
Ibn Ezra says people will trust God when they see that He was a stronghold for the oppressed, as the verse just before says. Radak says "You did not abandon those who seek You" means You were with them in their time of trouble.
Ibn Ezra and Radak on Tehillim 9:11From Yeshayahu 42:21:
יְיָ חָפֵץ לְמַעַן צִדְקוֹ יַגְדִּיל תּוֹרָה וְיַאְדִּיר.
Hashem wanted for the sake of His righteousness to make the Torah great and glorious