From my limited experience and knowledge of php;
It is your first error that is the offender and this creates the 'headers already sent' error. At least when I get this I look first to the initial error.
Was functions_email.php a file that was edited/changed? and/or is it this code for line#91 in your install?
Code:
while (strstr($email_text, $zen_fix_current)) $email_text = str_replace($zen_fix_current, $zen_fix_replace, $email_text);
Or could it be another file that might have been altered making an out of place call to the above?
I know that this is not the first time that you have setup 1.3.x...So you have most likely verified the MySQL, php, Apache etc on the host and your local has probably seen many installs.
Am I correct in assuming that the host install was setup up locally and copied to the host re-setting the required pathing & DB entries?