Did the battle between Scotland and Norway actually take place as depicted in Macbeth?

Yes. There was a Scottish-Norwegian war which lasted from 1262-1266 but this was not contemporary with Macbeth who lived two hundred years earlier. Scholars are less certain whether there were battles with the Norwegians during Macbeth's reign although such bickering was commonplace. The Norwegian king may have been Thorfinn Sigurdson, Earl of Orkney.