It is not supposed to be easy tweaking a multisite. I have been searching and testing a lot of ideas and solutions in order to accomplish this:
On the multisite frontpage I will have two columns (sidebars/asides) where column one should list the latest post from all members who are predefined to post in category 1. In the second list the latest post from all members who are predefined to post in category 2.
(This pre-definition is possible thanks to Author Category plugin. Thanks!).
The only plugin I found capable of doing the miracle I am looking for is the Network latest posts. Yes, this one gives me a widget where it is possible to separate the useres (as long as I remember which user belongs to which category). The widget is re-usable for more sidebars.
So far so good, but the drawbacks are:
1. I am getting really plugin dependent.
2. I can't style the output as I want. My wet dream is to list each of the latest posts along with the authors gravatar, the title, the date and a small excerpt.
Maybe the solution is to hire an incredible talented WP-coder. I am so stuck.