Will Drupal 8 Twig have template inheritance like Drupal 7?
I think you might be confusing inheritance with granularity. Twig actually does have the concept of template inheritance (see extends), while Drupal 7's theme engine doesn't.

The short answer is yes, you can expect the same from Drupal 8 as you did from Drupal 7. Specifically for fields, the example in the docs for field.html.twig will give you some insight:


  For example, for a field named 'body' displayed on the 'article' content type, any of the following templates will override this default implementation. The first of these templates that exists is used:
  
  field--node--field-foo--article.html.twig
  
  field--node--field-foo.html.twig
  
  field--node--article.html.twig
  
  field--field-foo.html.twig
  
  field--text-with-summary.html.twig
  
  field.html.twig


These can be altered/added to using hook_theme_suggestions_alter(), or the more specific hook_theme_suggestions_HOOK_alter().