This question has been answered by sottwell. See the first response.
(by the way: the pages wihout the .html are unstyled :S
<base href="[[!++site_url]]">
You are right! Thank you! But now some other questions arise (Maybe my questions seem silly...):
In the Friendly URLs section of System Settings, it's the 'container_suffix' setting.
(by the way: the pages wihout the .html are unstyled :S
Thats because you have linked to your CSS files relative, add the below before the closing in your template .
<base href="[[!++site_url]]">
Go to the Content -> Content Types menu. There you can see all of the provided content types and their extensions. The default for the HTML type is .html, but you can change that to anything you want.