Having created a similar search/query type database some years ago, (I presume that is what you are creating?). Mine had a few smaller php pages that all linked together. I wonder sometimes how I actually managed to make it work, but it did and looked fantastic. The styling I created myself which had its own CSS stylesheet and the layout was pure HTML within a PHP file, similar to how Moodle works.
I had it on my website for a while until it got hacked. At the time I did not know enough about security issues. So I learned the hard way. Lets face it anything on a server on the web is a target for hackers!
If all you want to add is the Header and Footer from the Adaptable theme, then I would be tempted to add the same php/html code as you find in the theme/adaptable/layout/columns1.php of your Moodle site.
That said, the Adaptable layout page I have just mentioned will only work inside Moodle, so if your SQL/PHP file is outside Moodle then you only need to copy the HTML for the header and footer and copy the CSS for those elements to get it to look like part of the site.
Does that make sense?