Attached screenshot of "disabled" buttons.

The dataPaginator provides facet based navigation. So it can not be supported by the component directly. In order to get it work the application needs to dynamically change the images when on pg. 1 or pg last, etc.

Excuse my ignorance, but I don't understand why the dotted lines appear.
I intend to use this component in my next project, so I don't appreciate such behavior.

Why the dotted lines appear?
When the paginator is already on the first page, then there is no benefit clicking on the following buttons:
-FirstPage
-FastBackward
-PreviousPage

That is why the dataPaginator disables those navigation buttons which doesn't have any effect based on its current page. Internally the commandLink renderer renders the iceCmdLnk-dis class for those links which are disabled. That allows you to visually change the disable buttons. You might you liked the current style which is dotted line but you can always override them. For example you can add the following style class to the application level css file:
.iceDatPgrScrBtn .iceCmdLnk-dis

or if you don't want to see any difference between enabled and disabled buttons then add the following style class to the application level css file:
.iceDatPgrScrBtn .iceCmdLnk-dis

Hope that will help.