After the fall of Sauron and Isildur's death, the one survivor of the Battle of the Gladden Fields made his way with the Shards of Narsil. To make a long story a bit shorter, the Necromancer moved into Dol Guldur about 100 years after this event, and some years after the Gladden Fields Minas Ithil fell and became Minas Morgul, which is when (give or take a little) Minas Anor became Minas Tirith (I'm pretty sure I have the names right). In the south, there was great fighting through all of Ithilien, during the time of the great plague, the assault of the wainriders (easterlings in wagons), and the Kinstrife, wherein Castamir took the throne from the current king, Eldacar, who was only half-Numenorean. Castamir took over Umbar (resulting in its becoming the city of the Corsairs) when he was driven from Gondor when Eldacar returned, defeating him in battle at Osgiliath, at which time the Palantír was lost.
Actually, there were three survivors, Minas Ithil fell in the year 2001, after Arnor was destroyed, and Umbar was founded before Minas Morgul was founded.
In the North, the descendants of Anarion (Elendil's other son) were ruling the realm of Arnor. The Witch-King arrived and began to build the realm of Angmar, slowly but surely shattering the power of Arnor until Arvedui, the last king, had to flee into the north. He vanished from history when an elven ship sent by Cirdan to pick him up failed to return home, as it was winter.
Anarion's descendants ruled in Gondor, Isildur's heirs (thus Aragorn's title) ruled Arnor, and as I said, all of this happened before Minas Morgul was created. He also had 2 Palantir with him when his ship disappeared.
The last king of Gondor, whose name escapes me at the moment, built a great fleet and sailed north to challenge the realm of Angmar. His army met the Witch-King in battle outside of Fornost, for the Witch-King would not await his onset. The Angmarian forces were routed, utterly, and while the Witch-King attempted to flee back to Angmar with what remained of his army, an elven host led by Glorfindel swept out of Imladris, while the cavalry of the Gondorians (which had not participated in the previous engagement) caught up with the Witch-King. The evil forces were annihilated, while the Witch-King personally faced the king, whose horse fled, bearing him away unwillingly. However, Glorfindel caused the wraith to flee back to Mordor.
Earnur wasn't King in Gondor at the time that he went north to help Arnor.
The descendants of Anarion became the Rangers of the North, while the King returned to MInas Tirith. He was later challenged by the Witch-King to single combat outside of Minas Morgul. Foolishly he accepted and was trapped and died. Thus began the reign of the stewards.
Again, it's Isildur's heirs who lived in Arnor.
Hope that helps.
Other than that, you are correct.
Why yes, I did own one of these. Back before they all became demon possessed.