To be precise in language, "federal government" means Article I legislative offices, Article II executive offices, and Article III judiciary offices, along with Article I-authorized lower courts. Article V conventions derive their authority from the same place as Article I, II, and III office-holders, the United States Constitution.
"Under authority of the United States" also includes the states themselves, since it is the people and the states that ordained and established the Constitution in the first place. I can't imagine a definition of "authority of the United States" that excludes the states themselves from authority. The Constitution has limits on what the federal government can do, and it has limits on what the states can do, but Amendments 9 and 10 made it clear that the states held supreme authority for anything not specifically delegated by them to the federal government.
To the second question, you are correct that there are many clones. So be it. The point is that the currently seated Article I office-holders cannot participate in an Article V convention without first resigning from their Article I offices.
-PJ
No, the Article 10 says “...the states and the people.” so it is not just the states, but also the people. And how would the people act? Through their personal lives, as well as through their elected representatives at state and federal level.
Example: Religion: States could have a state church, or not. MA still has a state church. Individual citizens could decide to go to church, or not. Federal government had, initially, nothing to do with it, except the commissioning of various chaplains as necessary and proper to other powers.