First, since the if (!function_exists('check_admin_referer')) echo "<h1>check_admin_referer not found</h1>"; code is working, then you’ve eliminated the issue being proper including of your Plugin sub-file.
Second, all four of those functions are core WordPress functions, so you should never get a call to undefined function error for any of them. Can you post your relevant Plugin code, so we can see what’s going on?
EDIT
My best guess is that certain functions aren’t available until certain actions within the WordPress processing sequence.
Try hooking your function into init, or admin_init, and see if the errors disappear.