I can only speak confidently to one of the items on your list but I suspect a pattern holds for all of them: it's true...ish.

I've answered questions about the relationship between American schools and Prussia (here, here, and here) but to recap, early systems of formal education - including common or public education - were present in the American colonies in the late 1600s. These schools were mostly shaped by colonizer's experiences in English schools and primarily focused on a classical curriculum.

Prussia didn't invent state-sponsored, formal education - it's a concept that emerged in a variety of societies around the world at a variety of times - but did create a structure of taxes, record-keeping, teacher training, and laws and policies that piqued the interest of American politicians and education advocates. Touring Prussian schools was a common experience for such men in the first half of the 1800s. These trips served as fact-finding missions and in many cases, the Americans came back with a sense of what not to do. The most notable example of this was a school leader from New York State who went to Prussia and wrote about how the Prussian system wouldn't work in NYS.

To the last part of your question - how did today emerge from yesterday - the clearest way to see that American schools aren't based on Prussian schools is to compare the modern American and German system. Virtually every American schoolchild experiences 13 years of a liberal arts curriculum - high school is four years of math, English, history, science, music, art, PE, etc. (there are some exceptions but they're not the norm). On the other hand, the modern German system - which evolved from the Prussian system - differentiates high school experiences based on a students' abilities and interests. Some schools are academic-focused, some are technical, others are vocational.

And one last point - you asked about who participated in conversations. American education is dominiated by women in the classroom but men in positions of leadership. Like many other aspects of American history, the primary decision makers and powerbrokers have been white men, mostly without disabilities. In the case of education, a great deal has been focused on keeping white children away from children of color, and denying children of color access to resources white children had and have.