Why doesn't the site open without index.php in the url (apache .htaccess)?

Question

Apache HTTP Server

Hello. There is a site on prestashop, the whole thing hangs on ubuntu 16.04 (VestaCP apache phpfcgi + nginx).
The site was transferred from nginx + php-fpm to the same Vesta, while at the same time it did not want to open in a new place using a regular link like www.example.com. Opens only at www.example.com/index.php otherwise it gives a page of Vesta with a bare inscription of my domain name.
Without CNC and enabled 301 redirect with adding "DirectoryIndex index.php" to .htaccess, it starts working without index.php
But it's worth turning on CNC and 301 redirect so that there are no duplicates, an empty page appears again I am
attaching the code from my .htaccess

<IfModule mod_rewrite.c>
<IfModule mod_env.c>
SetEnv HTTP_MOD_REWRITE On
</IfModule>

RewriteEngine on

DirectoryIndex index.php
RewriteRule . - [E=REWRITEBASE:/]
RewriteRule ^api$ api/ [L]
RewriteCond %{HTTPS} !=on
RewriteRule ^(.*)$ https://%{HTTP_HOST}/$1 [R=301,L]

RewriteRule ^api/(.*)$ %{ENV:REWRITEBASE}webservice/dispatcher.php?url=$1 [QSA,L]

# AlphaImageLoader for IE and fancybox
RewriteRule ^images_ie/?([^/]+)\.(jpe?g|png|gif)$ js/jquery/plugins/fancybox/images/$1.$2 [L]
</IfModule>

AddType application/vnd.ms-fontobject .eot
AddType font/ttf .ttf
AddType font/otf .otf
AddType application/x-font-woff .woff
<IfModule mod_headers.c>
  <FilesMatch "\.(ttf|ttc|otf|eot|woff|svg)$">
    Header add Access-Control-Allow-Origin "*"
  </FilesMatch>
</IfModule>

#If rewrite mod isn't enabled
ErrorDocument 404 /index.php?controller=404

Also, lines have been added to apache2.conf

<Directory /home/admin/web/site/public_shtml>
        AllowOverride All
        Options +Includes -Indexes +ExecCGI
        php_admin_value open_basedir /home/admin/web/site/public_shtml:/home/admin/tmp
        php_admin_value upload_tmp_dir /home/admin/tmp
        php_admin_value session.save_path /home/admin/tmp
        <Files *.php>
          SetHandler fcgid-script
        </Files>
        FCGIWrapper /home/admin/web/site/cgi-bin/fcgi-starter .php
    </Directory>

Answer 1

The issue was resolved by changing the .htaccess file

DirectoryIndex index.php
<IfModule mod_security.c>
SecFilterEngine Off
SecFilterScanPOST Off
</IfModule>

<IfModule mod_rewrite.c>
<IfModule mod_env.c>
SetEnv HTTP_MOD_REWRITE On
</IfModule>


# Disable Multiviews
Options -Multiviews

RewriteEngine on


#Domain
RewriteRule . - [E=REWRITEBASE:/]
RewriteRule ^api$ api/ [L]

RewriteRule ^api/(.*)$ %{ENV:REWRITEBASE}webservice/dispatcher.php?url=$1 [QSA,L]

# Images
RewriteRule ^([0-9])(\-[_a-zA-Z0-9-]*)?(-[0-9]+)?/.+\.jpg$ %{ENV:REWRITEBASE}img/p/$1/$1$2$3.jpg [L]
RewriteRule ^([0-9])([0-9])(\-[_a-zA-Z0-9-]*)?(-[0-9]+)?/.+\.jpg$ %{ENV:REWRITEBASE}img/p/$1/$2/$1$2$3$4.jpg [L]
RewriteRule ^([0-9])([0-9])([0-9])(\-[_a-zA-Z0-9-]*)?(-[0-9]+)?/.+\.jpg$ %{ENV:REWRITEBASE}img/p/$1/$2/$3/$1$2$3$4$5.jpg [L]
RewriteRule ^([0-9])([0-9])([0-9])([0-9])(\-[_a-zA-Z0-9-]*)?(-[0-9]+)?/.+\.jpg$ %{ENV:REWRITEBASE}img/p/$1/$2/$3/$4/$1$2$3$4$5$6.jpg [L]
RewriteRule ^([0-9])([0-9])([0-9])([0-9])([0-9])(\-[_a-zA-Z0-9-]*)?(-[0-9]+)?/.+\.jpg$ %{ENV:REWRITEBASE}img/p/$1/$2/$3/$4/$5/$1$2$3$4$5$6$7.jpg [L]
RewriteRule ^([0-9])([0-9])([0-9])([0-9])([0-9])([0-9])(\-[_a-zA-Z0-9-]*)?(-[0-9]+)?/.+\.jpg$ %{ENV:REWRITEBASE}img/p/$1/$2/$3/$4/$5/$6/$1$2$3$4$5$6$7$8.jpg [L]
RewriteRule ^([0-9])([0-9])([0-9])([0-9])([0-9])([0-9])([0-9])(\-[_a-zA-Z0-9-]*)?(-[0-9]+)?/.+\.jpg$ %{ENV:REWRITEBASE}img/p/$1/$2/$3/$4/$5/$6/$7/$1$2$3$4$5$6$7$8$9.jpg [L]
RewriteRule ^([0-9])([0-9])([0-9])([0-9])([0-9])([0-9])([0-9])([0-9])(\-[_a-zA-Z0-9-]*)?(-[0-9]+)?/.+\.jpg$ %{ENV:REWRITEBASE}img/p/$1/$2/$3/$4/$5/$6/$7/$8/$1$2$3$4$5$6$7$8$9$10.jpg [L]
RewriteRule ^c/([0-9]+)(\-[\.*_a-zA-Z0-9-]*)(-[0-9]+)?/.+\.jpg$ %{ENV:REWRITEBASE}img/c/$1$2$3.jpg [L]
RewriteRule ^c/([a-zA-Z_-]+)(-[0-9]+)?/.+\.jpg$ %{ENV:REWRITEBASE}img/c/$1$2.jpg [L]
# AlphaImageLoader for IE and fancybox
RewriteRule ^images_ie/?([^/]+)\.(jpe?g|png|gif)$ js/jquery/plugins/fancybox/images/$1.$2 [L]

# Dispatcher
RewriteCond %{REQUEST_FILENAME} -s [OR]
RewriteCond %{REQUEST_FILENAME} -l [OR]
RewriteCond %{REQUEST_FILENAME} -d
RewriteRule ^.*$ - [NC,L]
RewriteRule ^.*$ %{ENV:REWRITEBASE}index.php [NC,L]
</IfModule>

AddType application/vnd.ms-fontobject .eot
AddType font/ttf .ttf
AddType font/otf .otf
AddType application/x-font-woff .woff
<IfModule mod_headers.c>
  <FilesMatch "\.(ttf|ttc|otf|eot|woff|svg)$">
    Header add Access-Control-Allow-Origin "*"
  </FilesMatch>
</IfModule>

<IfModule mod_expires.c>
  ExpiresActive On
  ExpiresByType image/gif "access plus 1 month"
  ExpiresByType image/jpeg "access plus 1 month"
  ExpiresByType image/png "access plus 1 month"
  ExpiresByType text/css "access plus 1 week"
  ExpiresByType text/javascript "access plus 1 week"
  ExpiresByType application/javascript "access plus 1 week"
  ExpiresByType application/x-javascript "access plus 1 week"
  ExpiresByType image/x-icon "access plus 1 year"
  ExpiresByType image/svg+xml "access plus 1 year"
  ExpiresByType image/vnd.microsoft.icon "access plus 1 year"
  ExpiresByType application/font-woff "access plus 1 year"
  ExpiresByType application/x-font-woff "access plus 1 year"
  ExpiresByType application/vnd.ms-fontobject "access plus 1 year"
  ExpiresByType font/opentype "access plus 1 year"
  ExpiresByType font/ttf "access plus 1 year"
  ExpiresByType font/otf "access plus 1 year"
  ExpiresByType application/x-font-ttf "access plus 1 year"
  ExpiresByType application/x-font-otf "access plus 1 year"
</IfModule>

<IfModule mod_headers.c>
  Header unset Etag
</IfModule>
FileETag none
<IfModule mod_deflate.c>
  <IfModule mod_filter.c>
    AddOutputFilterByType DEFLATE text/html text/css text/javascript application/javascript application/x-javascript font/ttf application/x-font-ttf font/otf application/x-font-otf font/opentype
  </IfModule>
</IfModule>

#If rewrite mod isn't enabled
ErrorDocument 404 /index.php?controller=404