Is freedom from invasion of privacy a basic civil right?

You have a constitutional right to be secure in your persons and effects from unlawful search and seizure by the government. There is no "right to privacy".

Beyond that, you'll need to be a more specific to your situation. If you have somebody stalking, watching, or stealing your private information, it's possible there is criminal charges that can be brought against these people. You will have to check with local law enforcement.