How to add Alignment Tags to the Badge Image?

You want to use the theme system. Individual badges are themed using the theme label 'user_badge'.

Here's the current default theme function:

/**
 * Return html representation of a badge image
 * (note: theme_image does the check_plaining)
 */
function theme_user_badge($badge) {
  $image = theme('image', $badge->image, $badge->name, $badge->name);
  if ($badge->href != "") {
    return l($image, $badge->href, array('html' => TRUE));
  }
  else {
    return $image;
  }
}

For general instructions on how to override this theme function, you'll need the Drupal help pages and forums on that topic.