I would like to duplicate a shelf, so it will be displayed in monitor and laptop as well. How could I do it?

You cannot 'mirror' shelves, but you can certainly clone an existing shelf (but from then on any changes you make on one you will have to duplicate on the other) by right clicking the left mini-tab -> Dock and Shelf Management -> Duplicate Shelf.

You can also do this from the Dock & Shelves tab in Preferences.

You could also have discovered the answer for yourself just by exploring all the different options available in Preferences, which is nothing more than the obvious thing to do with any new programme.....

I can't see Dock and Shelf Management option. Do I need to have Winstep Nexus Ultimate to be able to do it?

When you said "shelf" I assumed you were running either Nexus Ultimate or Winstep Xtreme. If you are running the free version of Nexus then it's a "dock", not a "shelf", and in that case, yes, you need either Nexus Ultimate or Winstep Xtreme, since the free version only supports a single dock.