sunken city is a side quest. once you discover the death school and talk to ambrose he will send you to the tree, woh introduces you to the spiral door, and you can begin kroktopia. it helps to do the side quests to keep you levels high when you start new worlds, most players start kroktopia and come back to sunken city after they get their next spell. weekends there are usually alot of people waiting at the entrance to sunken city looking for people to go in with them.
Nope its a side quest but its good for XP! Thomas Asheyes Grandmaster Pyromancer
You do not need Sunken City to advance. It is an optional dungeon like many of the harder dungeons in the other worlds. You just have to complete wizard city to move on. I was in marlybone long before I beat sunken City. In fact, I just beat it yesterday to confirm my answer to you.. So no its not mandantory. I was level 35 when I completed it.