Journeyman,
While you may not have realized this, you have actually mixed three different types of prayer and offered them as an example as if there were all the same. This is common for those who come from a Watchtower background.
Jews, remember, had their religion and culture first, and then the Bible afterwards. This means the worship, rituals and prayers came first and these influenced what you find in the Scriptures, not the other way around. These prayers and rituals are called "liturgy," a formal structure of worship that Jehovah's Witnesses don't have, but other religions do, even other Christians like Catholics, Orthodox Christians, even Protestants like Lutherans and Episopalians and Anglicans.
The prayers of Jews are litrugical. The prayers in the Hebrew Bible are narratives.
Then you added the prayers of Jesus. These have nothing to do with Judaism. The instructions of Jesus fly in a total different direction of Jewish prayer at times, and sometimes contradict within themselves. There is some evidence to suggest that some of the instruction on prayer of Jesus comes directly from the Nazareth rabbi, but some of it might come from his followers. I will not cover that here, but the best thing to note is that you cannot mix Jewish with Christian and expect that they are the same thing. They are not.
Jewish views on prayer has changed over time as Judaism is not a static religion like Christianity. We are not based on the views of a central authority. Christianity cannot move away from its views due to it being based on the teachings of Jesus. Judaism is actually a civilization with a religion in it. The religious views are on a spectrum and evolve over time as the community grows and faces new challenges.
The Scriptures explain the views on God during various eras including the eras of Moses, the Judges, and the Prophets. The comprehension of God changes during each of these eras from an entity that creates to one that demands sacrifice and fights war to one that has no desire for the blood spilled on altars and wants all people from all nations to pray to Him. God is merely another "character" in the narratives of Scripture in order for people to relate to stories and learn their lessons. The prayers offered are no more genuine than the miracles.
Is God real? What is God? Is there a personal God? Does God require worship? Does God listen to prayer? What is the real purpose of prayer? Is prayer even necessary? Are there other ways to "pray"? This is what and how Israel worships today. The very word "Israel" means to "wrestle with God."
Judaism is not filled with answers like the Watchtower religion advertises. It is a means to ask questions, a healthy means to ask. You have to find your own and live with the answers you find. That is what Judaism teaches.
Christians like definitive answers. Jews do not offer those.
The search is part of the journey. The journey is part of what it means to be Jewish.