How can the author choose when to publish an article, whether the article gets a teaser or not? Is there a possibility for the author/editor to decide - when publishing - whether the article (the content type) gets a teaser or not? 
This is important for the look of the article on the front page.

I thought so far that would have to be defined before in the content Type.
If I understand your question, then this can be done by checking the Promoted to Frontpage box on the article. 

You can then change your view to filter out nodes that have Promoted to Frontpage checked.