At least states are pretty independent from the federal govmnt in the USA?
Not so much. Anything that includes interstate commerce falls under federal purview, and that definition has expanded greatly over time. Also the federal government has used the withholding of funding as a way to influence states. Finally there is the Supreme Court. It's possible abortion will become illegal. Oh, climate change and other treaties are negotiated by the Federal government.
This is a much more detailed and involved question, but the short answer is "kinda." States can do their own thing within the framework of the US Constitution and the Bill of Rights (in theory). But say, Ohio and Indiana have a ton of laws that are way out of step with each other even though they share a long border. "ObamaCare" was a state health care plan run by Massachusetts that was taken to the federal level, for example. Colorado has legal marijuana for recreational use, while Wyoming that shares a border with Colorado makes all possession punishable by jail time. If you think of the USA like the Eurozone with 50 countries and a really strong Brussels? that is more like what we are.