this is a basic question but I can't find any answer. It's driving me (a bit) mad.
When I press F12 the UV/Image-editor becomes my render-editor but how can I change it back to an UV-editor?
It is your UV editor, it's just showing your rendered image.
See the image popup at the bottom of the pane, that says "Render Result"? Just click that, and select another image.