Apple external Keyboard A1243 does not work properly
At minimum, your keyboard needs to be cleaned.  More than likely, it needs to be replaced.

Just doing a quick search for your symptoms brings up tons of relevant results in which a majority of the keyboards needed to be replaced.  Some were fixed by a cleaning, but that requires taking the keyboard apart.

But to be certain it is your keyboard and not you computer, just plug the keyboard into another computer; if the problem persists then it's time for a new one.