Just in case someone hits the same problem like me, I leave this post here.
DB navigator used to complain about missing certificates during booking process and refused to go to the booking page. Clearing the cache, uninstalling and reinstalling didn’t help.
As I have “AdAway” installed, I just tried to deactivate it, and magically DB Navigator started to work and let me book a ticket. Reactivating AdAway makes DB Navigator stop working. I started playing around in the Navigator and found that I had enabled “All cookies”. When I switched to “Only necessary cookies” (rough translation from German) DB Navigator works also with activated AdAway.
So it seems that some of my adblocking lists prevent placing of a strange cookie inside DB Navigator. (Which is a good reason to install AdAway…)
So, if DB Navigator refuses to work and complains about missing certificates, you could try to deactivate AdAway or only accept necessary cookies inside the application.