I see your on Windows? Then you must check the permissions not for you, but for the user (LocalSystem?) that Apache uses to execute.
On the errors, it seems that there might be a problem with the write permissions for one or all the xoops_data (sub)directories (see installation instructions).
Notice: Only variable references should be returned by reference in file /modules/smartfaq/include/functions.php line 588
Warning: MyTextSanitizer::makeTboxData4Show is deprecated in file /class/module.textsanitizer.php line 619
Warning: MyTextSanitizer::makeTboxData4Show is deprecated in file /class/module.textsanitizer.php line 619
Warning: MyTextSanitizer::makeTboxData4Show is deprecated in file /class/module.textsanitizer.php line 619
Warning: MyTextSanitizer::makeTboxData4Show is deprecated in file /class/module.textsanitizer.php line 619
Warning: MyTextSanitizer::makeTboxData4Show is deprecated in file /class/module.textsanitizer.php line 619
Warning: Cache Engine file is not initialized in file /class/cache/xoopscache.php line 180
Warning: Cache Engine file is not set in file /class/cache/xoopscache.php line 138
Warning: Cache Engine file is not initialized in file /class/cache/xoopscache.php line 180
Warning: Cache Engine file is not set in file /class/cache/xoopscache.php line 138
Notice: Only variable references should be returned by reference in file /modules/smartfaq/include/functions.php line 588
Notice: Only variable references should be returned by reference in file /modules/smartpartner/include/functions.php line 163
Notice: Only variable references should be returned by reference in file /modules/smartpartner/include/functions.php line 163
Notice: Only variable references should be returned by reference in file /modules/smartfaq/include/functions.php line 588
Warning: MyTextSanitizer::makeTboxData4Show is deprecated in file /class/module.textsanitizer.php line 619
Warning: MyTextSanitizer::makeTboxData4Show is deprecated in file /class/module.textsanitizer.php line 619
Warning: MyTextSanitizer::makeTboxData4Show is deprecated in file /class/module.textsanitizer.php line 619
Warning: MyTextSanitizer::makeTboxData4Show is deprecated in file /class/module.textsanitizer.php line 619
Warning: MyTextSanitizer::makeTboxData4Show is deprecated in file /class/module.textsanitizer.php line 619
Notice: Only variable references should be returned by reference in file /modules/smartfaq/include/functions.php line 588
Warning: MyTextSanitizer::makeTboxData4Show is deprecated in file /class/module.textsanitizer.php line 619
Warning: MyTextSanitizer::makeTboxData4Show is deprecated in file /class/module.textsanitizer.php line 619
Warning: MyTextSanitizer::makeTboxData4Show is deprecated in file /class/module.textsanitizer.php line 619
Warning: MyTextSanitizer::makeTboxData4Show is deprecated in file /class/module.textsanitizer.php line 619
Warning: MyTextSanitizer::makeTboxData4Show is deprecated in file /class/module.textsanitizer.php line 619
Warning: Cache Engine file is not initialized in file /class/cache/xoopscache.php line 180
Warning: Cache Engine file is not set in file /class/cache/xoopscache.php line 138
Warning: Cache Engine file is not initialized in file /class/cache/xoopscache.php line 180
Warning: Cache Engine file is not set in file /class/cache/xoopscache.php line 138
Notice: Only variable references should be returned by reference in file /modules/smartfaq/include/functions.php line 588
Notice: Only variable references should be returned by reference in file /modules/smartpartner/include/functions.php line 163
Notice: Only variable references should be returned by reference in file /modules/smartpartner/include/functions.php line 163