I don't know if hiding site roles will fix it but first just put another certificate instance in and see if it only has one name. Also check Administration> Appearance> Course managers to be sure only teacher role is selected there
If you have people assigned to the teacher role on a site level (generally not a good idea but there are reasons to do so) they may still appear in the certificates. To get around that in one moodle that I admin I created a duplicate of the teacher roll called it global teaching and assign those who I needed to have teacher ability in all classes to that role.
Now as to the odd certificates. If you are good with phpmyadmin or editing data bases in general you can delete them in mysql. Personally I love the free tool Scriptly if I want to edit a table.
Make a new certificate in the class and use login as each student who was already issued. It will have the current date (but it would if you delete the earlier ones anyway) if you do that. If you are not so hot on data bases it is at least user friendly