Change: Deleted the File field. Changed from jquery to Mootols. Added the File field.
Result: No errors.
Change: Changed from jquery to Mootools.
Result: No error now.
Do you mean you switched back to jQuery now and it works?
When I select the Joomla User (Andrew, Nina, etc.), and click save, it saves the file as Admin as the user
Do you mean it always saves as the Admin user? If so, I've not encountered this however, it would be worth testing this behaviour locally as these are pseudo-users.
Best wishes,
Gez