How can I check and connect HTML and PHP files, where the HTML file is stored on one system and the PHP file is stored on another servers machine?
How can I connect and transfer data between one machine and another, and how can I retrieve values from the remote PHP file?
It sounds like you need to take a look at AJAX.
jQuery have a some good documentation that will help to get you started.
This will allow you, from your HTML file, to retrieve content from another page (PHP) and show it in your page. The PHP file could interact with a database, or a number of other things.