Rule No. 1: A Jew must recite 100 Brachot each day.
The rule that a Jew must recite 100 Brachot each day is cited by Rav Amrom Gaon in his introduction to his Teshuva that became known as the first Siddur, Seder Rav Amrom Gaon.
סדר רב עמרם גאון (הרפנס) ברכות השחר-וסדר תפלות וברכות של שנה כלה ששאלת, שהראנו מן השמים, ראינו לסדר ולהשיב כמסורת שבידנו, כתיקון תנאים ואמוראים. דתניא ר' מאיר אומר חייב אדם לברך מאה ברכות בכל יום. ובגמרא דארץ ישראל גרסינן הכי, תניא בשם ר' מאיר אין לך אדם מישראל שאינו עושה מאה מצות בכל יום שנאמר ועתה ישראל מה ה' אלהיך שואל מעמך (דברים י', י"ב) אל תקרא מה אלא מאה. ודוד מלך ישראל תקנן, כשהודיעוהו יושבי ירושלים שמתים מישראל מאה בכל יום, עמד ותקנן. ונראה הדבר שנשתכחו ועמדו תנאים ואמוראים ויסדום.
Translation: The order of prayers and Brachot for the entire year that you requested, that has been shown to us by Heaven, we deem appropriate to set forth and lay out in the manner in which the tradition was passed down to us, as compiled by the Rabbis during the period of the Mishna and of the Gemara. In the Jerusalem Talmud we learned: it was taught in the name of Rabbi Mayer; there is no Jew who does not fulfill one hundred Mitzvot each day, as it was written: Now Israel, what does G-d your G-d ask of you? Do not read the verse as providing for the word: “what” (Mah); instead read it as including the word: “one hundred” (Mai’Eh). King David established the practice of reciting one hundred Brachot each day when the residents of Jerusalem informed him that one hundred Jews were dying every day. It appears that the practice was forgotten until our Sages at the time of the Mishna and at the time of the Gemara re-established it.
By introducing his Teshuva by referring to the rule that a Jew must recite 100 Brachot each day, Rav Amron was signaling that the Siddur is a guide to reaching that goal. Why was the rule instituted? So that a Jew thinks of G-d as King of the world at least 100 hundred times each day and during many of his activities such as arising, dressing, opening his eyes, washing his hands, taking care of his hygienic needs and eating.
Rule No. 2. A Bracha that is missing שם ומלכות is not a valid Bracha.
This is how the Talmud presents the rule:
תלמוד בבלי מסכת ברכות דף מ' עמ' ב'-גופא, אמר רב: כל ברכה שאין בה הזכרת השם - אינה ברכה. ורבי יוחנן אמר: כל ברכה שאין בה מלכות - אינה ברכה. אמר אביי: כוותיה דרב מסתברא, דתניא: לא עברתי ממצותיך ולא שכחתי. לא עברתי - מלברכך, ולא שכחתי - מלהזכיר שמך עליו, ואילו מלכות לא קתני. ורבי יוחנן - תני ולא שכחתי מלהזכיר שמך ומלכותך עליו.
Translation: It was stated above: Rav said that any Bracha in which the Divine Name is not mentioned is no Bracha. R. Johanan, however, said: Any Bracha in which G-d's kingship is not mentioned is no Bracha. Abaye said: The opinion of Rav is the more probable. For it has been taught: I have not transgressed any of Your commandments, neither have I forgotten. This means: ‘I have not transgressed’ so as not to bless You, ‘neither have I forgotten’ to mention Your name therein. Of sovereignty, however, there is no mention here. R. Johanan, however, reads: ‘Neither have I forgotten’ to mention Your name and Your sovereignty therein.
It is not difficult to explain why G-d's name must be mentioned in a Bracha. If G-d's name is not mentioned, the person is not thinking of G-d when he recites the Bracha. But why is it necessary to also refer to G-d as king of the world? It is the way Jews deny the truth of the types of religious belief that G-d created the world and then left it to run by itself.