Starting a Session or running a PHP script prior to outputting any HTML will not throw off the layout of a page. There must be some other explanation for why your form is not centered.
Look in your HTML markup.
What you may want to do is run the script and save the value that you will print out into a variable. THEN, if you are not redirecting the user, print out the opening <html> and <body> tags, etc, and then have PHP output the message in the page where you want it....
So, this line:
print "Cookie status: authorised-".$_COOKIE[auth];
Could be:
$message = "Cookie status: authorised-".$_COOKIE[auth];
Then, obviously, in your page, wherever you want to display that message, you can have:
print $message;
<sidenote>
Also, as a side-note, when you use non-numerical array keys, it is best to put them in quotes, unless they are constants or variables.
So, this: $_POST[username]
Is best written as: $POST["username"] or $POST['username'] (single or double quotes, whatever your preference...)
</sidenote>