WP is_user_logged_in() doesn’t work in integrated site

I am trying to integrate the WP functions in a external php file.

The problem is that user’s and login’s authentication functions like is_user_logged_in(), is_admin(), etc doesn’t work at all. However, Post’s functions are working correct.
So, it has to be a “Session” problem.

Actually after a deep deep search, the only “good” post in the web about the issue is the following old post in WP support: https://wordpress.org/support/topic/how-to-integrate-sessionlogin-authentication-to-non-wordpress-pages-w-wp-auth

But, that solution isn’t working at all, and if I enable the root Cookie plugin, I can not even login into my /wp-blog/

So, is there any idea how to integrate and the login functions in the php file?

Code is pretty simple:

file.php

<?php
//define('WP_USE_THEMES', false);
//include($_SERVER['DOCUMENT_ROOT'].'/wp-blog/wp-load.php');
include($_SERVER['DOCUMENT_ROOT'].'/wp-blog/wp-blog-header.php');

if ( is_user_logged_in() ) {
        echo 'logged in.';
} else {
        echo 'NOT logged in.';
}
?>

Also, I have the following warning in my error logs

PHP Warning: session_start(): Cannot send session cache limiter –
headers already sent (output started at /…./) in
/……/wp-content/plugins/global-content-blocks/global-content-blocks.php
on line 302

Edit:

I add the function.php as rnevius said in the comments

Code:

include($_SERVER['DOCUMENT_ROOT'].'/wp-blog/wp-blog-header.php');
include($_SERVER['DOCUMENT_ROOT'].'/wp-blog/wp-includes/functions.php');

and I have

the following fatal warning and fatal error:

PHP Warning: session_start(): Cannot send session cache limiter –
headers already sent (output started at /…./) in
/……/wp-content/plugins/global-content-blocks/global-content-blocks.php
on line 302

PHP Fatal error: Cannot redeclare mysql2date() (previously declared
in /…../wp-includes/functions.php:26) in
/……/wp-includes/functions.php on line 42

Edit:

Also, I have already tried it with all the following:

define('WP_USE_THEMES', false);
//include($_SERVER['DOCUMENT_ROOT'].'/wp-blog/wp-load.php');
include($_SERVER['DOCUMENT_ROOT'].'/wp-blog/wp-blog-header.php');

and

define('WP_USE_THEMES', false);
include($_SERVER['DOCUMENT_ROOT'].'/wp-blog/wp-load.php');
//include($_SERVER['DOCUMENT_ROOT'].'/wp-blog/wp-blog-header.php');

Edit:

This may help to think ideas:

We have the following structure:

domain.com/test/
domain.com/wp-blog/
domain.com/wp-blog/test/

If the file file.php if in the /test/ it doesn’t work.

domain.com/test/file.php
domain.com/wp-blog/
domain.com/wp-blog/test/

If the file file.php is in the /wp-blog/ it works!!

domain.com/test/
domain.com/wp-blog/file.php
domain.com/wp-blog/test/

If the file file.php is in the /wp-blog/test/ it works!!

domain.com/test/
domain.com/wp-blog/
domain.com/wp-blog/test/file.php

Every folder on the “domain” has 755 and files 644 permissions. So it is not a “permission” problem. any other thoughts?