You've got some sort of URL-Rewrite addon that's changing all the links to .html pages, instead of the actual real pages where they exist.
And, since you've not got the the infrastructure on your server for actually handling all the server-side translation of those links to their actual pages, your site is broken.
So, either turn off the URL-rewrite addon you've got installed (this is the most recommended approach, since URL-rewriting is not needed for search engines to index the site), or fix your missing translation instructions in your server configuration, such as .htaccess etc.
Failing this, get your hosting company to fix what they broke when they deleted your site.
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