Why does it say "God of" three separate times?
The words are not the rabbis' invention. In Shemot 3:15, God tells Moshe what to say to the Israelites: "Hashem, the God of your fathers, the God of Avraham, the God of Yitzchak, and the God of Yaakov, has sent me to you. This is My name forever, and this is how I am to be remembered in every generation." The Mekhilta (an early collection of rabbinic teachings on the book of Shemot) asks where this blessing's opening comes from, and answers with that verse.
The Ramban (Nachmanides, a medieval Torah commentator) reads "how I am to be remembered" as a promise. In every generation, whenever Israel mention "God of Avraham, Yitzchak and Yaakov," God will hear and answer them.
That still leaves the question: why repeat "God of" with each name? Rabbi Moshe Amiel (the Chief Rabbi of Tel Aviv, who died in 1946), in a sermon printed in 1936, says: each of them added something of his own to the Godliness he inherited from his father. So we say "our God and God of our fathers," he writes, because we may not settle for only our fathers' God. We have to reach "our God."
Tiferet Shlomo (a Chassidic book by Rabbi Shlomo Rabinowicz of Radomsk, Poland, printed in 1867) has a similar thought: each of the fathers brought his own side of Godliness into the world.
These are later readings. The verse itself does not say why the words repeat.
Shemot 3:15,Mekhilta DeRabbi Yishmael, Pischa 16:20,Ramban on Shemot 3:15,Sermons Unto My People (Derashot El Ami), The High Holidays 20,Tiferet Shlomo, on the Festivals, Yom Kippur 6Why is the Amidah whispered, and what if my mind wanders?
The rule for quiet prayer comes from a woman. Chana, praying for a child, was speaking in her heart. Only her lips moved, her voice was not heard, and Eli the priest thought she was drunk (Shmuel I 1:13). Rav Hamnuna reads laws from the verse: aim your heart, move your lips, do not raise your voice, and a drunk person may not pray (Berakhot 31a).
Why keep it quiet? Rabbi Yochanan, quoting Rabbi Shimon bar Yochai, says the Sages made the prayer silent so as not to embarrass people who have sinned. In the Temple the sin offering was slaughtered in the same place as the burnt offering, so no one could tell which kind a person had brought (Sotah 32b).
Does it have to be silent? A teaching in the Gemara says one who makes his voice heard in prayer is "of little faith." Abudarham explains: it is as if he thinks God cannot hear a whisper. Rav Huna limits the rule. It applies only to someone who can focus quietly. Someone who cannot may pray aloud, but only when alone, since in a group a loud voice disturbs others (Berakhot 24b).
And if your mind wanders? The Gemara teaches that one who prays should focus on every blessing, and if he cannot, then on at least one. In one version of the Gemara, Rav Safra, quoting a sage from the school of Rabbi Yehuda HaNasi (the editor of the Mishnah), says that one is this blessing (Berakhot 34b). Abudarham explains why: it holds God's greatness, the merit of the earliest generations, and the redemption of the later ones.
Shmuel I 1:13,Berakhot 31a,Sotah 32b,Berakhot 24b,Berakhot 34b,Abudarham, Weekday Prayers, Amidah