I've got a book I bought online - O'Reilly's Building Android Apps with HTML, CSS and JavaScript. The idea is that you can use these 3 to create a website that can be converted to an Android app by using a Java conversion tool.
Hopefully someone will be familiar with this, and hopefully this is possible - if I have a website that is already created that also includes PHP, could this be used for the app?
I've created PHP sites before, and the one I'm specifically looking at is referencing a MySQL database, hence my need to use PHP for the app. The website is heavily based on PHP.
No you can't (Unless you created your own framework which runs a local php server inside of the device which can be accessed by a webview). Php is a server side language. Html and JavaScript are client side. These html app creation frameworks use the webview to run apps. Be careful as there are performance issues when running through webview as it is not a native app (projects like crosswalk help but still many issues). Popular frameworks include ionic (Angularjs), titanium (is mostly native but from my experience limiting), and appgyver (Angularjs).
Yes you can! If by "converting" the website to app you mean displaying the website in a chromeless view mode (without address bar).
If you wan't to use phonegap / cordova you can still use the existing PHP code as backend for the database (Maybe rewrite it into a Restful API).
If you want your app to run natively and without internet connection, then you are out of luck though.