Scenario:
Because of an immense amount of php code and jquery widgets that php plugins weren't able to handle, I created a static page by saving the the page source of a wordpress page, inserting the php code, saving it (new.php) uploading it to root of site, creating a wordpress page (home2), pointing home2 to new.php using the "Pages Link To" plugin (http://wordpress.org/extend/plugins/page-links-to/) and then finally setting the newly created wordpress page (home2) that points to the static page (new.php) using this method: Settings=>Reading=>Front Page displays A Static Page (home2) (http://codex.wordpress.org/Creating_a_Static_Front_Page)

Here are my questions:

Question 1:
It appears that although new.php is not part of wordpress, the search engine works on the site. Why and how?
All the html states is that it is a form searching my site:

How can the searchbox actually work if new.php does not make any reference to the database?

Question 2:
Why does the right sidebar disappear if I put new.php in any location other than root of the site?

I am using:
Wordpress 3.0
Atahualpa 3.4.9
Also, although using 3.0 (appears to work), I have given my site its own directory:

http://codex.wordpress.org/Giving_WordPress_Its_Own_Directory
However, I have experienced similar 'issues' no matter version and template.