Why is the index.php file missing? I installed Drupal via the following command.
composer create-project drupal-composer/drupal-project:8.x-dev
projectfolder --stability dev --no-interaction

As a result I'm getting this structure.

../projectfolder/vendor/drupal
../projectfolder/vendor/bin/drush
../projectfolder/web/
etc. ...

Perfect structure, but what I'm missing the index.php file. Also, the common files like sites/default/settings.php are not part of my install or perfectly hidden.
How can I get those files? What I'm doing wrong? I tried to use Drush for an standard site-install, but it failed also.
That's exactly what drupal-project does. Your index.php should be at projectfolder/web/index.php.

Personally, I like this approach because it provides one directory level above your site root. This makes a good, secure place for files (settings, private file system) that should never be served directly by your web server. 

The drupal-project composer template uses this level above your  site root to install composer dependencies and tools like Drush and DrupalConsole. That's nice because when you bundle these tools with the project (instead of using a globally installed Drush for instance), you can always be sure that your colleagues are using the exact same version.