Yes, the watch will continue to tell the time for the time zone in which it was last connected.
When your watch is connected it will be automatically updated to reflect the time on your phone. Please see "My watch does not show the correct time" if the time on your watch is not correctly set.
The time on your watch reflects the time on your phone. Please ensure the watch and phone are connected and that the time on the phone is correct. In addition please check that you have the right time zone set in your phone for the second time zone to work as intended.
If the time on the watch is still incorrect you might need to recalibrate your watch. Open the Festina Connected app and tap Settings -> Calibrate watch. All hands should point straight up when calibration is done.
If you have been notified in the Festina Connected app about battery running low then please replace the battery.
No feature has been assigned to the Crown. Open the Festina Connected app and use the drag and drop feature next to the Crown in Watch face.