Greetings,
Is there a chance that the student was accidentally given the "teacher" or non-editing teacher" role in the course? you have probably already investigated this, but if not, check here:
Administration block > Users > Enrolled Users
Look to the right of the student's name and see what roles are listed.
On the submitting early problem, check the "Availability" setting in the Assignment's settings. The first item should be, "Allow submissions from". Students should not be able to submit work before the date/time you set here.
Good luck,
David
