Hi Flavia,
I recommend contacting your hosting provider, the 404 that is being displayed is your hosting’s 404 page instead of Wordpress. Which means the requests are not passing through for Wordpress processing, host only decides that it doesn’t exist.
And with that, there is no proper URL rewrite because the settings keep on adding index.php, and Wordpress automatically add it. The purpose of the rewrite is a catch-all-and-pass-to function so all requests are sent to Wordpress and so it will able to decide if it’s really a 404 or there if there is a function associated to it.
But, cornerstone works without URL rewrite, try editing a page and the builder will work but instead, the URL format will be like http://www.*******************.com/wordpress/?cs-launch=1&cs_route=content.builder/39
Thanks!