I leave the plug-in enabled (with the eye open), then disable it at the settinggs level?
Yes, you leave the eye open for Email-based self-registration and set 'Self registration' to Disable.
what about at "class level"
Here you are referring to Enrolments, which is something different from Authentication.
"The allowed email domain setting only affects new users, and not current users".
So, having this set would prevent anyone in the future from setting up an account unless it had (for example) "samgeppiwebsite.com" as the domain,.. correct?
Yes, that is correct.
So I also see that students are not getting the updates from the forum now thate I have made these changes ..
This sounds completely unrelated to the authentication settings.