The 2002 error is one that used to pop up for some because of their firewall....there was a solution on the beta forums but i havent seen any one else ever post about it. D: I was getting that error a lot during Early Access but then when it got to the release date I havent seen it until today. Try closing FFXIV and opening it back up. It worked fine for me once I did that.

A more dangerous solution is disabling your firewall.....but i'd rather not recommended that lol
I think on the forums the solution was a port, not too sure.