Trying to list user and post information from (wp_includes/post.php ) causes Fatal error

Please revert your WP core file and create a plugin instead. For this type of functionality, you can use the Publish Post hook.

Assuming your custom table is in the same database as WordPress, and you want to save the email address of the current user:

add_action('publish_post', 'update_my_custom_table');
function update_my_custom_table() {
    $current_user = wp_get_current_user();
    $email = $current_user->user_email;
    global $wpdb;
    $addInfo = $wpdb->insert('wp_custom_table', "$email");
}

Hopefully this will get you started down the right path, so you can insert whatever data you’re trying to add. There may be a better way than adding your own table, depending on what you’re trying to accomplish, but you didn’t mention much about your goal for the data.