Hi Peter,
1. Users can create accounts and enroll in several different ways. The account can be created by an admin (one at a time or via upload) or by the user signing up via email. Then you can have courses open to students enrolling (but you can set a key so that only students who are given the password can join the course). Teachers can also add students to a course (once the student accounts have been created
http://docs.moodle.org/en/Enrollment
2. Attendance can be done with a plugin. Search the database below for attendance. http://moodle.org/mod/data/view.php?id=6009 I haven't tried any of these out, but there are lots of ratings and comments. Also teachers could create an assignment to keep track of attendance if you can't add a module to your moodle.
3. A coach/teacher can enroll in a course whenever they want (as long as the course is set to be enrollable). Student data stays in the course even if you unenroll the students. (Of course you can reset a course to clean out student data to reuse it).
4. I am not sure what you mean by monitor/register sessions so some more detail on this would be great.
5. Keep asking questions in the forums -try to search the forums for similar topics. Also just play around with some course and user settings and then read Moodle docs. Folks will probably be willing to help you.