FATAL ERROR: WP complains about redeclaration [closed]

Wrap your function with !function_exists() to avoid a redeclare error.

if( ! function_exists('FAvideoid') ) :

  function FAvideoid()
  {
      return $wpdb->get_var( "SELECT 'video_id' FROM $wpdb->ytvideos ORDER BY RAND() LIMIT 1;");
  }

endif;

Or to reduce the code from being imported more than once:

include_once "FA-db.php";
include_once "FA-admin.php";
include_once "FA-ad.php";

But probably the best route is to mix the two:

// Only load files and hook events if your functions haven't been defined

if( ! function_exists('FAvideoid') ) :

    include_once "FA-db.php";
    include_once "FA-admin.php";
    include_once "FA-ad.php";

    add_action( 'admin_menu', 'FAmenu' );
    add_action( 'wp', 'FAad' );
    add_action( 'activated_plugin', 'FAsetup' );

endif;