When you enter your login data (DAV server URL, user name, password) in DAVdroid, the user name and password will be sent to the server you specified and nowhere else.
Contacts, events and tasks are stored by the respective Android content providers and not by DAVdroid itself. User data won't be sent to any other server than the given CalDAV/CardDAV server.
DAVdroid doesn't collect, process or transmit any statistical data like app or server usage. There are no ads and there's no tracking.
This Web site (DAVdroid Web site) doesn't collect or process personal data.
Visits are logged by the Web server. These logs are only used for maintenance purposes and to generate anonymous access statistics.