Grabbing $_POST data
To tackle your exact question, let me first tell you that what happens in the form is the correct thing. 

When you submit the form, it takes data, validates it and calls appropriate submit handlers to take care if the rest. 
The form, once its routing is completed, does a 302 redirect to the same location so a browser F5 hit does not resubmit data. 
It's a general practice to avoid double submissions. 

You will need to make a module that alters the form using hook_form_alter and alter the form. 

You can change form's action URL to the other PHP file or add an extra submit handler that posts data to the other raw php file using drupal_http_request. 

You will find sanitized and structures data in $form_state['values'] (second param of a submit handler is usually called $form_state). 
$_POST is also available at this stage.