I solved the problem with multiple languages with the help by user FredSchenk and the thread FAQ Manager - FAQs multiple times displayed.

The code in zen-cart\includes\modules\pages\faqs_all\header_php.php line 21-22 which reads:

$faqs_all_query_raw = "select p.*, pd.*, pcd.faq_categories_name from " . TABLE_FAQS . " p, " . TABLE_FAQS_DESCRIPTION . " pd, " . TABLE_FAQ_CATEGORIES_DESCRIPTION . " pcd, " . TABLE_FAQ_CATEGORIES . " pc " .
"where p.faqs_status = '1' and p.faqs_id = pd.faqs_id and pd.language_id = '" . (int)$_SESSION['languages_id'] . "' and p.master_faq_categories_id = pcd.faq_categories_id and p.master_faq_categories_id = pc.faq_categories_id and pc.faq_categories_status='1' ";

must be changed to read:

$faqs_all_query_raw = "select p.*, pd.*, pcd.faq_categories_name from " . TABLE_FAQS . " p, " . TABLE_FAQS_DESCRIPTION . " pd, " . TABLE_FAQ_CATEGORIES_DESCRIPTION . " pcd, " . TABLE_FAQ_CATEGORIES . " pc " .
"where p.faqs_status = '1' and p.faqs_id = pd.faqs_id and pd.language_id = '" . (int)$_SESSION['languages_id'] . "' and p.master_faq_categories_id = pcd.faq_categories_id and p.master_faq_categories_id = pc.faq_categories_id and pc.faq_categories_status='1' and pd.language_id = pcd.language_id ";