Ok, I put 'News' widget on my portal. In widget options i set the board of the news. It all works fine, except that 'News' widget doesn't display Sticky or Announcement posts of that board. It only displays normal posts, but not that "important" ones. Why is that?

That's just how that module works - that way you have an option to create global announcements even in the news section (for example a welcome or introduction thread) that would always appear in your news module.

I'm not quite sure I understood. You say that I can make announcement inside my 'News' widget? How? I mean, even if I could do that, it would be same if that widget just showed an announcement which is inside given board, wouldn't it? What I figured out is that I have to make completely new widget.

Sorry for being a little unclear, what I meant is that you can create announcements inside the forum that you use for your news module. They won't appear on the widget then.

Yes, i know they won't appear on the widget, my question is why?
It doesn't make sense, sometimes I have some important announcement that i want to be displayed on my portal, and for that i have to make whole new widged, instead of just making new announcement post in my board which would be shown in portal. Complicated, isn't it?