Why would I ask to be "like dust to everyone"? Isn't that being a doormat?
Taken alone, the line sounds like a request to be walked on: "To those who curse me, may my soul be silent, and may my soul be like dust to everyone." So it is worth asking what the Gemara means by dust, and by silence.
In Chullin 89a, the rabbis compare Avraham, who said "I am dust and ashes," with Moshe and Aharon, who said "What are we?" The Gemara calls the second greater. Then Rabbi Ile'a says the world stands only in the merit of someone who holds himself back during a quarrel.
Shabbat 88b says something close. It speaks of people who are insulted and do not insult back, who hear their shame and do not answer. About them the Tanach says that those who love God are like the sun coming out in its strength.
Notice what the line asks and what it leaves out. It asks for silence toward people who curse me, not agreement with them. Abudarham reads it as a step up: not only do I ask not to insult anyone first, I ask for the strength to bear an insult, as in Shabbat 88b.
On dust he gives a picture: everyone walks on it, yet it ends up on their heads, and in the end everyone needs it. So, he says, whoever lowers himself in this world will be at the head in the next. And a few lines later the prayer asks God to cancel the plans of people who plan evil against me. It is not giving up. It is holding your tongue and asking for help.
Tosafot (Gemara commentaries from France and Germany, 1100s and 1200s) add a second meaning of dust. Dust never comes to an end. So "like dust" can also be a hope that my descendants never come to an end, as in "your descendants will be like the dust of the earth."
Where the line falls between holding back and being a pushover, none of these sources says. They describe someone who hears the insult and chooses not to answer, not a rule for every case.
Chullin 89a,Shabbat 88b,Abudarham, Weekday Prayers, Amidah,Tosafot on Berakhot 17a,Bereishit 28:14I just finished praying. Why is there a whole second prayer after it?
The Amidah (the standing prayer) has 19 blessings. They are fixed: set blessings in a set order, the same for everyone. Elokai Netzor is the opposite. It began as one man's own words.
Berakhot 16b and 17a list several rabbis who each said something personal when they finished praying. Rava said: "My God, before I was formed I was not worthy. Now that I have been formed, it is as if I was not formed. I am dust while I live, and even more when I die." Rav Sheshet, while fasting, asked that the fat and blood he had lost to hunger count as if he had offered them on the altar. Mar's words are one more in that row. No two are alike.
The Mishnah Berurah (a central commentary on daily Jewish law, written around 1900) notes that in his region everyone was used to saying Elokai Netzor. So Mar's words became the shared version. But the same book quotes the Chayei Adam (a law guide by Rabbi Avraham Danzig, Vilna, early 1800s), who says it is proper and fitting for every person to pray each day, in particular, about their own needs and livelihood.
So the answer is the Gemara's own picture. After the fixed words, rabbis added words of their own, and each one is different. The siddur keeps Mar's, and the spot after it is still open for yours.
Berakhot 28b,Berakhot 16b and 17a,Mishnah Berurah 122:1 and 122:8Why does a prayer about my mouth end by asking God to rebuild the Temple?
The last request is that "the Temple be rebuilt speedily in our days." After a prayer about my own mouth and my own enemies, that can feel like a jump.
The Rema (Rabbi Moshe Isserles, Poland, 1500s) explains why it sits here. Prayer stands in the place of the Temple service, so we ask for the Temple, so that we can do the actual service. The Kitzur Shulchan Aruch (a short guide to daily Jewish law, 1860s) repeats his words. The idea goes back to Berakhot 26b, where Rabbi Yehoshua ben Levi says the prayers were set to match the daily offerings. Another rabbi there says the patriarchs set them, so the Gemara does not give only one origin.
You can see what the Temple meant to one rabbi on the same page as Mar. Right after Mar comes Rav Sheshet, finishing a fast. When the Temple stood, he says, a person who sinned brought an offering. Only its fat and blood were offered, and he was forgiven. Now I have fasted, and my own fat and blood have shrunk. May it be Your will that this count as if I offered them on the altar. He is asking to be treated as if he had what the altar once gave.
Our line asks for a second thing too: "give us our share in Your Torah." The Rabbi Yishmael prayer ends with the same request and shows its shorter form in Pirkei Avot 5:20. Our version ends with words from the prophet Malachi, "as in the days of old and as in years long past."
The Rambam (Maimonides, Egypt, 1100s) rules that the Messiah will rebuild the Temple and that sacrifices will be offered again. Why God would want sacrifices at all is a hard question of its own, and the Tamid prayer takes it up. The sources here explain what this line asks and why it sits at this spot. They do not tell you how to feel about it.
Shulchan Aruch, Orach Chaim 123:1 (Rema),Kitzur Shulchan Aruch 18:12,Berakhot 26b,Berakhot 17a,Pirkei Avot 5:20,Malachi 3:4,Rambam, Laws of Kings 11:1