Assuming you are using the old plugin (mod_certificate) -
In the certificate settings you should be able to list other emails you wish the certificate to be sent to.
RE: the email address being used - looking at the code it seems to use a teacher's email (if there are multiple it grabs the first one (no idea why but that is what it does - I didn't write the initial code for this plugin )), which if invalid uses the setting 'noreplyaddress' (search for this setting in the site administration search), if that hasn't been set it uses noreply@<yourhost>.
If you want to change this then you will have to make modifications to mod/certificate/locallib.php and look for the function responsible for emailing.
HTH,
Mark