Set the search index and the field_revision_body empty I'm not using the core Drupal search engine and I'm not using any revisioning on my nodes.  I noticed that the {search_index} table and {field_revision_body} table are occupying 50Mo of my database space.

Does emptying these tables cause any problems?
You shouldn't empty field_revision_body as it will break the content, but search_index is ok to empty.

Regarding search, please review the settings at: /admin/config/search/settings

e.g uncheck the Node and User search under "Active search modules"