There are a couple of things that occur to me, I noticed that you have 'All categories' selected, as well as the individual categories, it is possible that this might cause a problem, try unselecting 'All categories'.
If that does not solve it, you need to be clear that, if you want to display results from a particular category or categories on an individual tab then you need to set the category ids on the individual 'Tab Ids' parameter, if you don't set these then no result will be returned.
The menu item that allows you to select K2 categories to filter results is used to filter by category when other tab types are being used, for example if you want to show random or latest news items, and only want them to show results from particular categories. If you use this filter then it will be applied to all the tabs - it is possible that this behaviour is causing some confusion. Note that if you use a category tab, and the category ids are different from the filter category then no result will be returned. I might think about changing this behaviour, it might be more helpful for the filter to be ignored in this case.
I hope this makes sense. The module is designed to be very flexible, but that does mean it gets quite complicated.
I am sure this can be solved though.