If I forward an appointment imported from Google Calendar to a different day in my Daycast, will the change show up in my Google Calendar?

No. This integration syncs data in one direction: from Google Calendar to Daycast. If you’d like to make changes to events in Google Calendar, you must edit the event in Google Calendar. We’ve made this easy: Just click the Google Calendar icon in the far right of your task field and you’ll be taken directly to the event in your browser where you can make any changes you like.

Changes you make to calendar items in Daycast will remain only in Daycast.