I created a DAVdroid account on my android device and selected the calendar for synchronisation, but it does not show up in DAVdroid (i.e. when I go to settings->accounts->DAVdroid->XYZ).
What does that mean? It shouldn’t show up there. Just use your calendar app. Or what exactly are you missing there? Do you mean “calendar sync” is not available there, but “contacts sync” and “tasks sync” are?
I had a look at the logcat, and as far as I can see, DAVdroid does not even attempt to synchronise the calendar entries, although it does synchronise the contacts and tasks successfully.
Sounds like the synchronization is disabled, either because the sync interval is set to manually or for some other reason.