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1) This error:
PHP Strict Standards: Non-static method Protector::getInstance() should not be called statically in /xoops_lib/modules/protector/include/precheck_functions.php on line 12
indicates that you have an older version of XOOPS that doesn't support your PHP version. You probably have PHP 5.4.x and either:
a) XOOPS older than 2.5.6, or
b) you have XOOPS 2.5.6 but you have not updated the files in /xoops_lib
So please either install XOOPS 2.5.6, or update the files in /xoops_lib
2) The error about memory could have different reasons. If you have access to it, try to change your php.ini file, and increase the available memory, and see if it helps.