There seems to be a problem with your DNS resolver (or the SRV records were temporarily down):
2017-05-03 22:07:22 397 [ui.setup.DavResourceFinder] Looking up SRV records for _carddavs._tcp.fastmail.com
2017-05-03 22:07:37 397 [ui.setup.DavResourceFinder] Didn't find carddav service, trying at https://fastmail.com:443
$ host -t SRV _carddavs._tcp.fastmail.com
_carddavs._tcp.fastmail.com has SRV record 0 1 443 carddav-d277161.fastmail.com.
It should work with these settings: https://davdroid.bitfire.at/configuration/fastmail/
Can you try this with your connection? Can you try another connection type (WiFi/mobile)?