Allow user to translate specific field? I have a content type called profile where a user can enter data and thereby create an own profile. Now, most of the profile fields are numeric but two of them are text areas. As my site is in German and English the user should be able to translate these two text area fields (the Input not the Label) but no other fields.

Does somebody know if there's a way to grant translation access to users for specific fields?
Entity translation will do the trick :). That module allows you to point out certain fields to be translated without translation the entire node.

https://www.drupal.org/node/1280632 shows you some use cases and examples on how to configure the module.