(1) Is addon also called module?
(2) How can I enable / disable a module (e.g. downloads)?
 

A module is called an addon.
In you admin area highlight Structure, then choose addons. You should then see a complete list of all your addons, choose delete or uninstall downloads.

Thanks Paul, to be more precise though…

Addons may contain modules. Often the name of an addon is the same as the main content module it contains, e.g. downloads and downloads.

If you want to get rid of the downloads module you'd typically uninstall the whole downloads addon. Otherwise you could turn off permissions to access the downloads page (all modules are pages).