The website support service is actually superior to the in-game petition service: there is more room to explain your issue, and more options to help specify what your ticket is about and who it should be directed to.
The petition service downtime will allow the GMs to process the backlog of tickets we currently have and improve response time for all players.
You don't have to log in or create an account to contact support, just provide an email address. If the form linked above won't let you past a login prompt, try this one (https://help.ncsoft.com/app/ask).
What about petitions that have already been send vie In-Game system and awaiting for response?
Ones that are in are the ones they'll be addressing. :)