You're using HTML where PHP is expected. That's why you have a blank screen.
Here's how I'd move this into a shortcode:
function wpse_shortcode_userlevel() {
global $current_user;
get_currentuserinfo();
$output = '<span class="shortcode-user-level">';
$output .= $current_user->display_name . "\n";
$output .= "Level: {$current_user->level} \n <br>";
$output .= '</span>';
return $output;
}
add_shortcode( 'userlevel', 'wpse_shortcode_userlevel' );
Then in your stylesheet add:
.shortcode-user-level {
color: #ff0000;
}