Disables the theme update checking and notification system.
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 theme update notifications to be shown to the users of these installations. This plugin is for them.
Yes. Please see the Disable WordPress Plugin Updates plugin.
Yes. Please see the Disable WordPress Core Update plugin.