Dear Flemming,
In your example, a 'Course' is a 'Course' in Moodle, but it is also the instance with a specific starting / ending date if set. 'Classes' are really 'Groups' (http://docs.moodle.org/24/en/Groups) if you consider a class to be a collection of attendees. But I do not believe there are specific group enrolment dates but I'd have to research that - http://docs.moodle.org/24/en/Course is a good place to start to learn about courses.
In terms of enrolment for a specific activity / resource, you can restrict access based upon certain conditions, but I don't think enrolment is a part of it, see http://docs.moodle.org/24/en/Conditional_activities_settings. But it is possible to restrict access to activities / resources by using 'Groupings' - groups of groups (http://docs.moodle.org/24/en/Groupings) - where a group can be in one or more groupings.
Cheers,
Gareth