So I just bought eye of the north.

And when I go to the character creation screen there is no eye of the north icon. Is this because there are no new characters for eye of the north just content? Sorry if this sounds dumb im new to guildwars just wanted to try the first game out before the second one is released.

Also is there any surefire way to know that the game is correctly installed?

I preinstalled the game, however I didnt have a cd key, I later bought eye of the north through the ingame store and everything seemed to work correctly.

Eye of The north is an expansion not a campaign. So you are correct in assuming you can not create a character to start in it. You can go to the North after you reach level 10 and if you do go before 20 you get temporarily "buffed" so that you won't get totally destroyed. It is great content to do after you have beaten the other three campaigns but you can really do it anytime after level 10.

The quests to get there once you reach level 10 are in Kamadan, Kaineng Center, and Lions Arch. You only need one to get there, not all three. Hope this helps!!!

You don't start Characters in Eye of The North(EoTN or GW-EN) because it's an expansion versus the other games being campaigns. Characters you have created(and have reached level 10) can venture here for extra content that is happening after the events of all the other campaigns. You don't need to beat the other campaigns to get here, just be level 10 and have reached 1 or more of these towns: Kamadan:Jewel of Istan(Nightfall); Lion's Arch(Prophecies); or Kaineng City(Factions)

I would recommend finish the normal campaign first, since EOTN is a bit more difficult to do and even after the buff to a lvl 20 char the attribute points cannot be set afaik. This may result in a different char than you are customed to play.

If you want to make the normal campaign a bit easier you might wanna go untill gunnars hold and unlock some additional heroes.