The reason that the hierarchy is not documented is because it doesn't matter where in the site it is, it just needs to stay in that same structure. Wherever the contact form is the remaining files/directories need to be in that same level.
As far as copying the contact form page to one of your own pages, you were probably getting an error because you did not have the included files in your site at the correct place.
One other thing you can do instead of copying all the contact form code into your existing page is make changes to the contactus.php or contact_styled.php and then link to the contactus.php/contact_styled.php instead of your existing page. If you're not using templates, modifying the contact page to suit your needs is the same as modifying any other page.