Error logs - Can you help me fix them please

I am getting the following errors re a blogging page I loaded. I would appreciate it if you could help me with any of them.

1. PHP Deprecated: Non-static method PARSER::setProperty() should not be called statically, assuming $this from incompatible context in /home/mary/public_html/blog/nucleus/libs/ACTIONS.php on line 85

2. PHP Deprecated: Non-static method PARSER::getProperty() should not be called statically, assuming $this from incompatible context in /home/mary/public_html/blog/nucleus/libs/BaseActions.php on line 143

3. PHP Deprecated: Non-static method TEMPLATE::fill() should not be called statically, assuming $this from incompatible context in /home/mary/public_html/blog/nucleus/libs/BLOG.php

4. PHP Strict Standards: Non-static method MANAGER::instance() should not be called statically in /home/mary/public_html/blog/nucleus/libs/globalfunctions.php on line 145

5. PHP Deprecated: mysql_connect(): The mysql extension is deprecated and will be removed in the future: use mysqli or PDO instead in /home/mary/public_html/blog/nucleus/libs/sql/mysql.php on line 63

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