If you want to notify non users, then you can set up an Open Type Notification. A Notification of type Open can go to any email address even if they are not a user.
Notifications will only fire when a record is modified and saved, not via the simply passage of time to a new day.
So the typical solution is to have a Key user like yourself receive a daily report of Notifications due to be fired. Then we can make a formula URL button to sort of tickle the record to get it to fire a Notification and refresh the report with one less record on it, as the Notification was just fired. Then you click again and again until all the records are gone off the report.