Yes, to cancel an event via the API, you can send a POST request to the cancel event endpoint.
At this time, there is no API endpoint that supports rescheduling an event or invitee, however the cancel and reschedule URLs are on the invitee resource.
However, the cancel and reschedule URLs can be found on the v2 API webhook payload as well. You can see an example of the payload here.
These URLs are always inserted at the bottom of calendar events or email confirmations, but they are available on the API to be more easily retrievable so you can place them wherever you want in the app that you are building.
Please note that cancel event endpoint can be used to cancel an event, including a Group event, but not an individual invitee in a Group event.
