If I forward an appointment imported from Office 365 Calendar to a different day in my Daycast, will the change show up in my Office 365 Calendar?

No. This integration syncs data in one direction: from Office 365 Calendar to Daycast. If you’d like to make changes to events in Office 365 Calendar, you must edit the event there. We’ve made this easy: Just hover over the Office 365 Calendar icon in the far right of your task field and you’ll see a text link of your event. Click the link to go directly to the calendar 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.