So.. this is the furthest down I've gotten:
I have no clue what to do there. All I do is cheese my way slowly forward by building these tunnels.. The enemies kill you very fast if they get a hold of you, the lava is obviously lethal, and even the red buildings hurt you if you walk on/in them! So basically I dig my way down for an hour, look at the dangerous things and then teleport my way back to my safe house.
I did break down slightly, however. I looked up some recipes (on http://wiki.terrariaonline.com/ ) and how to build a house. The depth meter is new.
It definitely helps to have a house. I can't get the game to recognize my new house as my spawn point (despite following the instructions on the Wiki), but other than that it's a success. Ugly as hell too.