How do I translate menu link URIs? Is there a way to translate a menu link URI? 

When I change it in one language (e.g. http://www.example.com), it is also changed in the other language, where I want a different domain (e.g. http://www.example.de). 

Link title and description is working as expected.
It is not possible to translate the menu uri itself. If you want different menu links per language you need to create a unique menu per language, and use block visibility settings to limit each menu block to its respective language.

See this Drupal 8 multilingual hack for a step by step guide: build unique menus per languages