It was something with the caching. I went to the search caching options, cleared the cache, disabled the image cropping, now I'm getting 0.5 second responses, the performance tracker confirms as well: https://i.imgur.com/v4pxgBf.png
It should respond in 0,5 – 2 seconds on the front-end, based on the amounts of plugins (32) active and the site load time (~9 seconds: http://tools.pingdom.com/fpt/#!/eOLKYn/http://www.kommunen.dk/ ).
If you want to return authors (users) as results, you can enable it on the General Options -> User Search panel: https://i.imgur.com/LWsaxS7.png
The index table only affects post, page and custom post type search. The author data there means that it indexes the author name, description to posts created by him, so looking for the author name should return his posts.Best,
If you like my products, don't forget to rate them on codecanyon :)