do more action after I publish a post

There are a number of hooks you can use, such as publish_post or save_post, e.g.:

// an example of a post save hook
add_action( 'save_post', 'diligents_post_save_hook' );
function diligents_post_save_hook( $post_id ) {
    //verify post is not a revision
    if ( !wp_is_post_revision( $post_id ) ) {
        // do things
    }

}

save_post will fire on publish and update, so be aware it will fire on saving of drafts etc. publish_post will run on publish, keep this in mind as it will not fire on update.

Saving data to a file is a step I cannot cover, as it is not a WordPress question, but a standard PHP question. For details on writing, reading, and saving to files, reference PHP.net