Disables WordPress core update checks and notifications.
Most people will not want to (and should not) disable this feature. It's a fantastic feature of WordPress and I'm fully in support of it. However, administrators who maintain multiple installations of WordPress on behalf of other people (eg. clients) may not want update notifications to be shown to the users of these installations. This plugin is for them.
Yes, this plugin completely disables all core update checks, so the automatic update system will be disabled too.
Yes. See the Disable WordPress Plugin Updates plugin.
Yes. See the Disable WordPress Theme Updates plugin.