» How do I know that my votes are private on the VVPAT and that there is not a database in a computer somewhere that records how I have voted?

There is no way for the system to tie your vote to you. When you vote, there is no identifying information recorded with your vote (you'll notice there are no identifying numbers printed on the VVPAT printout). You will be given a randomly generated four-number access code tied to the particular ballot you should receive, based on your precinct number. But the access code is not associated with your name. Therefore, it is impossible to trace your vote. Additionally, the printed summary of your ballot will scroll out of view once your vote has been cast.