If I load a PHP page with Jquery .load(file.php), can the included file use the php variables that were defined on the page that called the load()?
Yes, use the data parameter, see http://api.jquery.com/load/:
$('#someelement').load( "test.php", { 'key1': '', 'key2': '' } );
The parameters are posted to the file test.php and are accessible as:
test.php
$_POST['key1'] $_POST['key2']