How to translate custom fields in taxonomy terms?
If you use 'Localize' option for taxonomy translation mode, it is possible to add taxonomy custom fields to string translation: 


/**
 * Implements hook_i18n_string_list_TEXTGROUP_alter().
 */
function YOUR_MODULE_i18n_string_list_taxonomy_alter(&$strings, $type, $object) {
  if ($type == 'taxonomy_term' && $object) {
    if (isset($object->FIELD_NAME)) {
      $term_FIELD_NAME = field_get_items('taxonomy_term', $object, 'FIELD_NAME');
      $strings['taxonomy']['term'][$object->tid]['FIELD_NAME']['string'] = $term_FIELD_NAME[0]['value'];
    }
  }
}


After clearing cache the field will be available in translation form.