Something I noticed. You're using the forward slash instead of a question mark... the params redirect would normally look like this:
RewriteRule ^(.*)$ index.php?params=$1 [L,QSA]
This should work by itself since any of those files *should* be real files.
ErrorDocument 404 /index.php
RewriteEngine On
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule ^(.*)$ index.php?params=$1 [L,QSA]
To have the site ignore specific extensions you can add a condition to ignore case and only check the end of the filenames in the request:
RewriteEngine On
RewriteCond %{REQUEST_URI} !(.css|.js|.png|.jpg|.gif|robots.txt)$ [NC]
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule ^(.*)$ index.php?params=$1 [L,QSA]
If you're trying to ignore a folder then you could add:
RewriteEngine On
RewriteCond %{REQUEST_URI} !(public|css)
RewriteCond %{REQUEST_URI} !(.css|.js|.png|.jpg|.gif|robots.txt)$ [NC]
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule ^(.*)$ index.php?params=$1 [L,QSA]
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