Theming

The theming is wrong.
Change all call to the theme functions with : theme('function_name', params); This way the theming will depend on the theme of the project if this theme implements this theme functions. Right now if you want to change the theming of the form and the results you have to change the module and that is a problem cause in future you can'i update it.

For drupal 6.* :
Add hook_theme in the code to describe the theme functions you use:
function sphinx_theme(){
return array(
'sphinx_results' => array(
'arguments' => array('results' => array(), 'index' => NULL, 'needle' => NULL, 'show_excerpts' => NULL),
),
'sphinx_feedback' => array(
'arguments' => array('results' => array(), 'needle' => NULL),
),
'sphinx_result' => array(
'arguments' => array('node' => NULL, 'excerpt' => NULL, 'fields' => array()),
),
'sphinx_excerpt_result' => array(
'arguments' => array('node' => NULL, 'excerpt' => NULL, 'fields' => array()),
),
);
}