As you can see in the logs, the TCP connections have been refused. This is a server or firewall problem and very likely not a problem of DAVdroid. Please contact your administrator, or if you are the administrator, fix the network problems.
Understand that you have to go to the caldav item and click on it before the calendar appears in the calendar app. How do I enable it by default without having to click on it? Any where in the code that I can modify to do so?