I'm a little bit further now. What I did was:
- Deleted all Services in Azure.
- Deleted all Storage Accounts in Azure
- Removed my Service-Project completely from solution (not the library containing the worker-logic).
- Re-added storage-accounts in Azure.
- Re-added services in Azure.
- Re-added a project in the solution and added the worker-logic inside it.
- Builded up all the publishing-stuff again.
- Published it.
The first publish ended like the one described in my question. After I checked the "Update development..."-option in properties of my worker it finally took my transitions into the stage!
Now I recognized, that WADLogsTable was still empty. I hit the instance right in server-explorer and choosse "Update diagnostic settings...". There was an option "Transfer period" suddenly set to "None". This explained to me, why my table was empty and after I set it back to "1" my table is filling again!
Another funny thing beside: When I right-click my Cloud-project in the solution I get "Object reference not set to an instance...". When I just click it left and choose Build->Publish it works.
I just hope that I can help somebody with this. Lets see if it's stable now.
Edit: Yesterday it worked - today is still the same issue :-(.