It does not work when installed as "subsite" I tried to install Drupal 8.03 on a windows 7 64 bit server, with MySQL, Apache and PHP 7.03, using the default install procedure / script.

Drupal is only one of the applications on the website and that is probably different from what Drupal 8 seems to expect.

The website is like https:/www.mysite.nl and overall root folder is x:\myroot\homepage. Drupal, however, is installed in x:\myroot\homepage\drupal and it is supposed to be accessible via https:/www.mysite.nl/drupal.

Back to the installation. To a "certain" extend that seems(!) to work. That will say the install script runs and ends. But than I want to access Drupal and that does not work. I can not access any thing "page missing". Both the base folder and the base url is not what Drupal expects (e.g. Drupal generates https:\www.mysite.nl\xyz where that should be https:\www.mysite.nl\drupal\xyz and I can not change that (at least not from the UI which is not accessible, assuming there is a setting for that).

So drupal seems is completely lost, does not understand what its base url is and does not understand where the files are (both at least the url should be a question during installation!!!!!).

By the way I never really used other drupal versions, but from a last year test install my impression is that this problem did not exist in drupal 7.

I do not know how to solve this. Hope you can help and perhaps initiate a few corrections/extensions in Drupal 8.
Look for this code in the .htaccess file in the root of the Drupal site's filesystem:

# Modify the RewriteBase if you are using Drupal in a subdirectory or in a
# VirtualDocumentRoot and the rewrite rules are not working properly.
# For example if your site is at http://example.com/drupal uncomment and
# modify the following line:
# RewriteBase /drupal


and remove the '#' from the beginning of the RewriteBase line. That should tell Apache/Drupal how to properly rewrite URLs for your case.