Yes, webhooks created through Zapier are available to free SuperSaaS accounts.
Manually created webhooks that connect without using Zapier are only available to paid SuperSaaS accounts.
The "Change appointment" trigger will trigger upon any change made by anyone. This includes changes made to it by the administrator including, for example, deleting an appointment or moving it out of the trash.
It also includes automatic changes, such as payment status change or a placement from a waiting list because a spot became available. For this trigger to be useful you will want to filter it on the "event", "role" and/or "status" fields. The "event" field will take a value that is one of create, edit, place, pending, destroy, restore, approve or revert. The "role" field will have a value of 4 or more for a change made by a superuser or the administrator. More details on the values of these fields can be found in the SuperSaaS documentation.
SuperSaaS schedules can be configured to either require signup before making a booking, or to allow booking directly without any log in. If a schedule does not require the end-user to sign up then you will never see a "New User" trigger, just a "New Appointment" trigger.