Now, on to the fight: America is explicitly NOT a democracy.
Yes, it is. You even say so yourself:
America is a democratic Republic.
"Democracy" in modern parlance == "democratic republic". When the word "democracy" is used in regular conversation, NO ONE is talking about Athenian-style direct democracy, unless they explicitly say so. It's only pedants like you who even think of this.
It was formed that way EXPLICITLY to prevent mob rule.
Democratic republics exist for several reasons. One is because no one citizen can possibly be competent at voting on every single issue that faces a large and populous nation, nor can every citizen be expected to invest that much time into the governing process. So we "outsource" most of the work of governing to politicians called "representatives", and elect them to represent us and do our bidding. The rules you talk about do exist to make sure there's a longer feedback loop, so people's short-term reactionary tendencies don't make a mess of things, and so that there's a rule of law: people have to follow laws, until the laws are changed.
The Constitution and Bill of rights spell out what America is supposed to be. If there is a true need for the Republic to change the rules it is built upon, then there are mechanisms in place to do that... but THEY HAVE NOT BEEN USED.
Yes, they have. The Constitution has been amended dozens of times since it was written, and countless Supreme Court cases have further changed laws. And if you have some kind of problem with a court effectively legislating and deciding law, then you have a problem with English Common Law, which this country was explicitly founded upon.
Why? We can argue about that forever. Regardless, the basic rules from which all other rules rest upon, have not been changed. That means a police state is incompatible with American law; both in the letter and spirit of the law.
Completely incorrect. If case law and legislation (at all levels of government) have resulted in a police state, then a police state is indeed compatible with American law, by very definition.
It's sad how poorly educated in basic Civics most Americans are these days.