I don't see any results in the search
Ensure that you linked your JSD project with a Confluence space.
I don't see results from some spaces
Ensure that you select all needed spaces in the app configuration.
How can I make sure no sensitive information is exposed?
You are the boss of your Confluence spaces, and this is up to you which spaces you select to be and not be visible to the world. The app only widens search capabilities but this is done for the Confluence spaces that are visible to public already and even those you can limit in the app settings.