I might not make it to the end of the fast. Is it a lie to say "on the day of our fast"?
The authorities treat these words as a statement that has to be true. The Shulchan Aruch (the main code of Jewish law) reports a view that an individual says Aneinu only at Mincha, the afternoon prayer. The fear is that he will get faint, have to eat, and turn out to have lied in his prayer.
They fix this in different ways. On the four fasts the Sages set (Tisha B'Av, 17 Tammuz, the Fast of Gedaliah and 10 Tevet), the Shulchan Aruch says even a person who ends up eating can still say it, since it is still the day the Sages set.
The Rema (Rabbi Moshe Isserles, who added Ashkenazi practice to the Shulchan Aruch) records that the custom on every fast is for an individual to say it only at Mincha. The Taz (a commentary on the Shulchan Aruch, Poland, 1600s), quoted in the Mishnah Berurah (a central commentary on Jewish law, around 1900), adds that someone who wants to say it in the morning may skip the words "on the day of our fast."
What about "our" when you keep a private fast alone? The Rema says to keep the plural. The Mishnah Berurah says it is not a falsehood, because it cannot be that no one in the world is fasting today. Some later authorities prefer "my fast" or "the fast," but the custom follows the Rema.
And the leader? The Tur (a code of Jewish law from the 1300s) quotes a teacher, Rav Natan, who said a leader who is not fasting cannot lead, since he cannot say Aneinu. The Tur disagrees. He points out the leader says "this fast day," and the fast belongs to other people, though a leader who is fasting is better when one can be found. But the Shulchan Aruch rules that on a public fast, a leader who is not fasting should not lead.
So the sources do not agree on the fix. What they share is the worry itself: the words of a prayer are supposed to be true when you say them.
Shulchan Aruch, Orach Chaim 565:1, 565:3 and 566:5,Mishnah Berurah 565:5 and 565:8,Tur, Orach Chaim 566If God answers before we even call, why do we have to pray?
The prayer asks God to answer us "even before we call to You." Then it quotes the verse where God promises exactly that: "Before they call, I will answer. While they are still speaking, I will hear" (Yeshayahu 65:24).
Radak (Rabbi David Kimchi, Provence, around 1200) starts with the verse's first word. He says it is the opposite of what Eichah (Lamentations) said about exile: "You have wrapped Yourself in a cloud so that no prayer can pass through" (Eichah 3:44). The verse is a promise that the cloud lifts.
Radak also notes the verse has two parts: sometimes God answers before they call, and sometimes while they are still speaking. Metzudat David (a commentary from the 1700s) says the first is when God fills the wishes of the heart before anyone prays out loud.
Ibn Ezra (a Spanish commentator of the 1100s) reads the verse differently. In his view the word terem here is like od, "still," and the promise is that God will give them whatever they ask.
The Rambam (Maimonides, who died in 1204) says who is answered this way. A person far from God cries out and is not answered. Once he has repented, he cries out and is answered at once, and the Rambam quotes this verse.
None of these sources says calling out is pointless. Each reads the verse as a promise about how God answers people who call. The question of why the call is still needed stays partly open: the sources describe what an answer looks like, not why it starts with us.
Yeshayahu 65:24,Radak and Ibn Ezra on Yeshayahu 65:24,Metzudat David on Yeshayahu 65:24,Eichah 3:44,Rambam, Laws of Repentance 7:7Why does the leader get a whole blessing, while I squeeze mine into someone else's?
On a public fast, the leader's repetition of the Amidah has Aneinu as a separate blessing, between "Who redeems" and "Who heals." When you pray quietly, even on a public fast with the whole congregation, you say it inside Shema Koleinu, the blessing that ends "Who hears prayer," with no closing blessing of its own. The Mishnah Berurah states the rule in one line: only the leader was given a blessing of his own, not individuals.
Why only the leader? The Tur reports what his father, the Rosh (Rabbeinu Asher, Germany and Spain, around 1300), wrote. The eighteen blessings were set by the prophets and are not to be changed. But a congregation that takes a fast on itself is certainly a public, and a public can set a blessing.
So the right to add a blessing belongs to a community, not to one person. That is why there are conditions. The Tur adds that ten people must be fasting. The Shulchan Aruch rules that they must be in that synagogue: ten fasters elsewhere in the city do not count.
The practice was not always taken for granted. The Tur records that some early rabbis were puzzled by what the early communities relied on to add Aneinu for fasts the community had declared on itself. The Rosh's reply is the principle above.
For an individual there is no new blessing, only a few added words inside an existing one. These sources do not say why a community's blessing needs ten fasters. They only say that it does.
Mishnah Berurah 565:2,Tur, Orach Chaim 566,Shulchan Aruch, Orach Chaim 566:3