Slim application 404 error with multiple .htaccess

Question

I'm trying to install an application based on the slim micro-framework on my local server (LAMP) but there is a redirection problem in the configuration. The project architecture is as followed :

project

-/admin
    -/app
    -/config
        -config.php
    -/public
    -/vendor
    -/composer.json
    -/composer.phar
    -/public
        -/assets
        -index.php
        -.htaccess(3)
    -.htaccess(2)
-/css
-.htaccess(1)

The content of my .htaccess is :

.htaccess(1)

# Allow any files or directories that exist to be displayed directly
<IfModule mod_rewrite.c>
    RewriteEngine on
    RewriteRule (.*) localhost/project/$1 [R=301,L]
    RewriteRule ^$ admin [L]
 </IfModule>

.htaccess(2)

# Allow any files or directories that exist to be displayed directly
RewriteCond ${REQUEST_URI} ^.+$
RewriteCond %{REQUEST_FILENAME} \.(gif|jpe?g|png|js|css|swf|php)$ [OR]
RewriteCond %{REQUEST_FILENAME} -f [OR]
# RewriteCond %{REQUEST_FILENAME} -d [OR]
RewriteCond %{REQUEST_FILENAME} -l
RewriteRule ^ - [L]
<IfModule mod_rewrite.c>
    IndexIgnore *.zip *.jpg *.gif
    RewriteEngine on
    RewriteBase /admin/
    RewriteRule ^$ public/index.php [L]
    RewriteRule (.*) public/index.php?/$1 [L]   
</IfModule>
php_value upload_max_filesize 1000M
php_value post_max_size 2000M
php_value memory_limit 3000M
php_value max_execution_time 180
php_value max_input_time 180

.htaccess(3)

<IfModule mod_rewrite.c>
    Options -MultiViews
    IndexIgnore *.zip *.jpg *.gif
    RewriteEngine On
    RewriteBase /admin/
    RewriteCond %{REQUEST_FILENAME} !-f
    RewriteRule ^ index.php [L]
</IfModule>

The config.php is used by the app for all env variables. The file is configured as following :

<?php
/* Server info */
define('MODE', "development");
define('APP_NAME', 'appname');
define('SERVER_URL', 'localhost/');
define('BASE_URL', SERVER_URL . 'project/admin/');
define('UPLOAD_URL', SERVER_URL . 'upload/');

define('BASE_FOLDER', '/var/www/html/project/admin/');
define('SERVER_FOLDER', '/var/www/html/project/');
define('APP_FOLDER', BASE_FOLDER . "app/");
define('TMP_FOLDER', BASE_FOLDER . "tmp/");
define('LOGS_FOLDER', BASE_FOLDER . "logs/");
define('UPLOAD_FOLDER', SERVER_FOLDER . "upload/");

define('FOLDER_NAME', "admin");
date_default_timezone_set('UTC');

/* Require */
require_once '../vendor/autoload.php';

When I try to access localhost/project/ I'm redirected to localhost/project/admin which is fine but I get an 404 not found. When I try to access directly localhost/project/admin/public/index.php , I have the menu displayed and still the 404 not found error as in the following image :

I think I have severals issues in this configuration :

1 - to get the localhost/admin/public/index.php page requesting localhost/admin/

2- To have the localhost/admin/public/index.php working fine with no 404

It is working fine on the production server, but I can't get the app working on my local server. I modified the .htaccess files and the configuration files When I run the app on my server, I have NO error in my /var/log/apache2/error.log I don't understand the issue with my configuration, any help ?