Parenting in the USA [closed]

My company wants me to temporally do some project in the USA (6months). I want to take my family with me. We raise our children quite independent.

For example: The oldest (7) is allowed to many things on her own (like meeting friends outdoor), she can even go tome some places without asking (playground in the neighbourhood). The younger (5) is allowed to this stuff with supervision of his older sister and some things on his own (like buying milk from the neighbourhood store). The youngest (2) will be trusted to stuff together with the oldest (like they shop in one store and I shop in the one next to it). They are also allowed to wear what they want (and if they not want to wear any clothes they are allowed).

Now my wife read this (from the foreign ministry of Germany)

https://www.auswaertiges-amt.de/DE/Laenderinformationen/00-SiHi/UsaVereinigteStaatenSicherheit.html

Which essentially says that all this is intolerable in the US and one would even face legal consequences (for some of things mentioned above). Of course our children will probably be not allowed to do that much in the first time. (Note that there will be hardly any language barrier, as my wife is Australian and speaks to the children in English)

But is it true that this rules are enforced (children are not allowed to be on their own before 8/12) and we could face legal consequences in the USA if we parent our children their in similar style? Also will their be any problems if we allow our children to be without clothes in public?

If this is true I might have to refuse doing this project.