Cannot make htaccess redirect www to non-www - apache

Question

The 3 comments in the code explain fairly accurate what I want to achieve.
<IfModule mod_rewrite.c>
RewriteEngine On
# Change secretdiary.org/index.php?url=URL to secretdiary.org/URL on the browser's url
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule ^(.*)$ index.php?url=$1 [PT,L]
# Redirect http://www.secretdiary.org/ to http://secretdiary.org/
RewriteCond %{HTTP_HOST} !^secretdiary.org$ [NC]
RewriteRule ^(.*)$ http://secretdiary.org/$1 [L,R=301]
# Add trailing slash / if there's none
RewriteCond %{REQUEST_URI} !(/$|\.)
RewriteRule (.*) %{REQUEST_URI}/ [R=301,L]
</IfModule>
However, I am finding some problems and I think they come from putting the conditions together. When I enter www.secretdiary.org/about , it gets (showing it in the browser) to secretdiary.org/index.php?url=about, deleting the www but ignoring the first rule. Switching the order did not help at all nor messing with RewriteBase. However, if I enter normally without the www, the uri is shown normally, secretdiary.org/about, without any rewriting. Why is this and how can I fix it?
Besides, I've followed this answer and this other attempting to add automatically a trailing slash to the uri if missing. I could achieved it with PHP ( if (substr($_GET['url'], -1) != "/") header("Location: " . htmlspecialchars($_GET['url']) . '/');, but now it bothers me that I cannot achieve it with .htaccess, so if you could also spot where's the problem here it'd be very helpful.

Answer 1

Try this .htaccess code :
RewriteEngine On
# Change secretdiary.org/index.php?url=URL to secretdiary.org/URL on the browser's url
RewriteCond %{HTTP_HOST} ^secretdiary.org$ [NC]
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule ^(.*)$ index.php?url=$1 [L]
# Redirect http://www.secretdiary.org/ to http://secretdiary.org/
RewriteCond %{HTTP_HOST} !^secretdiary.org$ [NC]
RewriteRule ^(.*)$ http://secretdiary.org/$1 [R=301]
# Add trailing slash / if there's none
RewriteRule ^([^/]*)[^/]$ $1/ [R=301,L]
I'm not sure for the last rule.

Answer 2

The main problem I faced was with Firefox storing the 301 redirect, which made the changes in .htaccess "not work". I deleted the cache and now it's working perfectly, although I made the trailing slash to be added with PHP to avoid headaches.
.htaccess:
<IfModule mod_rewrite.c>
RewriteEngine On
# For some shady reason, this redirect should be first.
# Redirect http://www.secretdiary.org/ to http://secretdiary.org/
RewriteCond %{HTTP_HOST} !^secretdiary.org$ [NC]
RewriteRule ^(.*)$ http://secretdiary.org/$1 [L,R=301]
# Change secretdiary.org/index.php?url=URL to secretdiary.org/URL on the browser's url
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule ^(.*)$ index.php?url=$1 [PT,L]
</IfModule>
index.php:
<?php
// Redirect if there's no trailing slash
if (!empty($_GET['url']) && substr($_GET['url'], -1) != "/")
{
header ('HTTP/1.1 301 Moved Permanently');
header ("Location: http://secretdiary.org/" . htmlspecialchars($_GET['url']) . "/");
}
// The rest of the php