Is there any way to capture calendar events like Cancel or move from office365? 1. Can we use some kind of add in here which will keep on listening to these events and if user canceled some appointment it provide us those appointment details and we can pass it to our internal application.
To me, it sounds like a better solution is to use REST API events to listen to updated calendar items (or created, deleted, etc.) and let your server application handle the events rather than have an add-in do it, especially since we do not have support for a "perpetual" add-in that is open all the time.
You can find more information here: https://msdn.microsoft.com/office/office365/api/calendar-rest-operations#Updateevents
To actually answer your question though, no, we do not have support for event listeners in the add-in platform as of yet.