How to display this meta data (an array) in form of a function (created with a custom write panel)?

Try this?

<?php        
function get_project_services() {    
         global $post;
         $data = get_post_meta( $post->ID, 'project', true );
         $project_services = $data['project_services'];    
         return $project_services;    
}
?>

Then in your template file:

<p><?php echo get_project_services(); ?></p>

I think that will do what you’re asking?

(Edited to match your comment.)