Enrolment

For the student issue, when you view the course Participants does it say "suspended" next to these students' names (or were they simply suspended at the "site level" via the Browse All Users page, in which case doesn't affect course enrollment). For the teacher those look like the Insight emails. Maybe someone turned on the insight system? An easy fix is to edit the Messaging preferences (Site administration - Messaging - Notification settings) and change "Insights generated by prediction models" to Permitted but uncheck the "online" and "offline" boxes -- then click Save Changes. Note that this will update the default messaging preferences of all site users, so if they've modified their own settings, they will have to modify them again, but this is a quick way to ensure the teachers won't get the emails (without disabling the entire Analytics system -- with no emails, the teachers can still see these reports in their course admin block). If you'd rather disable the entire Analytics system, go to Site administration - Analytics - Analytics models and you can click Actions - Disable next to each one.