How can I get to Kunark? Do I have to do some quests or something? Or can I just jump on a boat like live? Also is there any fun content there to do as a solo/duo?
You have to do an attunement quest/event thing, Ikisith. I think you can go a couple times for "free", but am not sure if thats still in game. I would search the forums. I think someone posted a full walk through or video a year ago.
For things to do, look up the murk and remnants of old ikild to start. There is tons to do there, including world nameds that regrettably are seldom done.
Kunark is 55+ areas (mostly 65+). You get there by doing the solo hatefury zone, which starts in NWOT (NRO of live). You are best off duoing there, unless you play a kiting class (watch out for summoning mobs though).