Unless said property literally floats in a vacuum, there are many public externalities arising from your use of your property.
Yes. The US is set up to permit regulation on federal, state, and local levels. It's one of the main roles of government.
And since it is only the U.S.'s regulations that make a particular piece of property "yours" rather than "no one's", arguing about the legitimacy of said regulations is incredibly daft. In the absence of regulations, you don't have any property at all.
The only reason anyone owns anything is because of government regulations?
That's an interesting take on the philosophy behind private property rights.