I am trying to configure a Content Search web part for a team site on SP13 online. There is nothing wrong with the query ("test query" works fine) but when i save the web part it is not showing any results.
I suggest you add your SP online site to your trusted sites. If the query works in the Test is something with the client side code, and trusted sites could fix it. If not, try to use the "debug" display template and see if show something.