If we have no shows or someone cancels is it best to mark them as such and leave them on the schedule? Or does that count against us? Or, is it better to just delete them?
We recommend that you do not make any changes to your procedures to satisfy alerts. Whatever you generally do for your no-show or cancellation appointments is what you should continue to do. If your procedure is to delete the no-show appointment, then yes, that will satisfy the alert. If you leave these clients on the calendar you will not get "credit" for their alert, but this is also why we do not recommend a 100% compliance rate for your stats!
Another option is to send the client a Direct Message (email or text). You can mention something similar to this "We're sorry we missed you today! We would love to help reschedule your appointment for Fluffy. Our records show that Fido is also coming due for an appointment - would you like to schedule an appointment for him/her as well?" Sending the Direct Message will allow you to address both the missed appointment and the other Alerts that are due.