Hey JH_,
Thanks for reaching out!
If you are asking if the configuration you presented is possible, it does indeed seem possible with WordPress and The Events Calendar.
However, The Events Calendar itself, nor any of our plugins, handle the creation of these various account types and all that.
You would have to find other plugins that help you make the roles for “Teacher”, “Student”, etc. – here’s an example of one such plugin that might help https://wordpress.org/plugins/members/.
If you’re interested in how to set up user roles and all of that, this is general WordPress-related information and so your best option is to explore http://codex.wordpress.org, or Google searching and similar research like that.
I hope this information helps!
— George