Disable Plugin and Theme Update and Installation
If you really want to disable Updates and Installations, you can block users from installing/updating themes and plugins through the dashboard. Add this quick snippet to your wp-config.php file:
define('DISALLOW_FILE_MODS',true);
It will prevent users from installing and updating themes and plugins. It will also automatically disable theme and plugin editing in the dashboard.
define('DISALLOW_FILE_MODS',true);