creating a static HTML/JS/PHP page

i need to create a static page that allows me to code HTML/JS/PHP…

Create a custom page template and integrate your structure in it.

.. that connects to a separate MYSQL backend.

I don’t know why you want a separate MySQL backend. In your comment, you tell that you’re making a contact form. I guess you’ll want to save messages in your database. You could just create a table manually in PHPMyAdmin (or make a plugin that does it for you).

You can then use the WPDB Class to easily connect to your current database and manipulate data in your added table.

As a side note, I strongly recommend you to prepare your queries before any operation.