I must produce a completely functional page inside my WordPress application (that will have jQuery along with other stuff). However , after i produce a file inside my theme/starkers (I am while using Starkers Theme) directory let say about.php the next links (during my index.php) aren't effective:

<li><a href="<?php bloginfo('template_directory'); ?>/about.php">About</a></li> <-- Fatal error: Call to undefined function get_header() 
<li><a href="about.php">About</a></li> <-- site not found

What's the easiest way to do this becasue I believe I can not add PHP and jQuery along with other complex stuff within the Pages that may be produced in Wordpress Admin.

Any suggestions?

What's the easiest way to do this becasue I believe I can not add PHP and jQuery along with other complex stuff within the Pages that may be produced in Wordpress Admin.

Why don't you? Simply make a custom page template within your theme, produce a new page in your wp-admin, and assign that custom page template for the page. You need to have the ability to personalize that around you would like.

Consider using a scan here : Wordpress Template Hierarchy : Pages

Try loading

require( '/path/to/your/wordpress/wp-load.php' );