How to show random feed from DB and show content in my site

It’s difficult to answer this, but here are some suggestions:

  • Make sure your feeds are valid, e.g. here.
  • In the case of is_wp_error( $rss ) giving true, you can check the corresponding error message with $rss->get_error_message().
  • Develop with WP_DEBUG activated.
  • Don’t use mysql_query(), it’s deprecated since PHP 5.5.
  • Use the $wpdb object to fetch data from your custom table.
  • Escape/prepare your SQL if it uses any user input, to avoid SQL injections.
  • Indent your code to make it more readable.
  • Remove the wp_reset_query() line, it’s doing nothing after the return.

Then update your question accordingly with more info. Thanks.