You can easily cancel or reschedule participants who have either been invited or confirmed by looking for a red cancel button after clicking on their interview spot from Scheduling >> Calendar. You'll notice the layer will look different depending on if they are confirmed (top image below) or if they have only been invited (bottom image below).
For rescheduling, there are two options, 1) proposed new time and 2) choose a new time which is letting the participant select a new time themselves. Simply drag the confirmed time to a new time during that week or another week.
If you test rescheduling yourself as a participant, which is a great idea, always use a fresh browser/incognito window to reschedule yourself as a test. Otherwise, you'll be logged in as you, which a participant would never be, and Ethnio will be all sorts of confused.
Make sure you've customized the cancel email under scheduling >> emails, which looks like below: