Is Entity Translation module compatible with Internationalization and can they be used to translate menus? I installed the entity translation module for Drupal 7 and it works fine.

However, I also want to translate menus and I found that Internationalization module can do that. 

The question is: are they compatible at all? If I install internationalization module will it not break the entity translation one?
Yes, they are compatible.

Entity Translation deals with entity translations, and menus in Drupal 7 are not entities, there's no clash between Entity Translation and Internationalization modules.