I can’t reproduce the problem with duplicate tasks here. So, please provide steps to reproduce, debug info and verbose logs.
Probably pressing synchronize button several times could be a clue to reproduct the issue?! If so I’say just prevent clicking while synchronizing and show a Status information.
No, synchronization is managed by Android’s ContentResolver. DAVdroid only requests the sync, and regardless of how often it is requested, it will not be run simultaneously for the same account/content authority.