Take a deep breath
Have you used an enrolment plugin? If so which one?
If not, sounds to me like you have assigned your teachers a role of teacher for the entire site, rather than in the context of your course. See this MoodleDoc Role FAQ page. I would also review all the Role links in the template on the upper right corner of that page in MoodleDocs.
As for the student button, what version of Moodle are you using? If it is 1.9, you are not going to see one. You may want to use the Assign Roles link in the course admin block to manually enroll students. This will also be the place you will removed those teachers you automatically added to your course (how ever you did it
). Hope this helps, I once held my breath for 3 days until some helpful person answered my post.
Best Chris