How to customize the node edit form? I need to customize the access to details like 'Publishing options', 'menusettings', 'authoring information' etc while the user is editing the node. 

These options should be shown only if the admin has allowed the users to view those. I Have searched for this, but unfortunately found no answers for Drupal 8.
You can use Simplify 


  Simplify allows particular fields to be hidden from the user
  interface. This helps to de-clutter forms and present a more
  user-friendly experience to content editors.




Enable the module, then go to People >> Permissions and check mark View hidden fields for the user role you want to allow to see them.