How to keep the protection and add the correct redirect from www to non-www?

Question

htaccess

When going to the page www.site.ru/page/test
Redirect to site.ru/index.php/test
When going to the page www.site.ru
Redirect to site.ru/index.php with error 404

I understand the problem with part of the code where index.php is specified, but if you remove it, pages other than the main one give an error 404

How to keep the protection and add the correct redirect from www to non-www ?

RewriteEngine On

RewriteCond %{QUERY_STRING} (\<|%3C).*script.*(\>|%3E) [NC,OR]
RewriteCond %{QUERY_STRING} GLOBALS(=|\[|\%[0-9A-Z]{0,2}) [OR]
RewriteCond %{QUERY_STRING} _REQUEST(=|\[|\%[0-9A-Z]{0,2})
RewriteRule ^(.*)$ index.php [F,L]

RewriteCond %{REQUEST_FILENAME} !-f
RewriteRule ^.*$ index.php 

#Редирект с www на без www
RewriteEngine On
RewriteCond %{HTTP_HOST} ^www.site.ru$ [NC]
RewriteRule ^(.*)$ http://site.ru/$1 [R=301,L]

Answer 1

RewriteEngine on
  # www to non-www
  RewriteCond %{HTTP_HOST} ^www\.(.*)$ [NC]
  RewriteRule ^(.*)$ https://%1/$1 [R=301,L]
  # http to https
  RewriteCond %{HTTPS} off
  RewriteRule (.*) https://%{HTTP_HOST}%{REQUEST_URI} [R,L]

  RewriteCond %{REQUEST_FILENAME} !-l
  RewriteCond %{REQUEST_FILENAME} !-f
  RewriteCond %{REQUEST_FILENAME} !-d
  RewriteRule ^(.*)$ index.php [L,QSA]