I have now 1280x1024 screen and recordmydesktop made a video with that resolution. What I can do to remove at least top & bottom black bars? What project settings?

What resolution do you want your final video in? You could try this
Set a project settings to that resolution. Use a pan and zoom effect to shrink your input video to fill screen.
Render the footage to the resolution choosen in step one.

That was the answer. But I changed the monitor and PC and recorded on better resolution...