please download the i485 instruction sheet. Most of the questions you have are answered in the instruction sheet. 
You will be filing for i485 only after your case number is current. Chicago office is known to reget your application for filing too early. I would not file one month early unless case number is current say for example very end of fiscal year like 2014 August or September. Individual case might varies but Chicago office usually expedites the case to forward to local office for any DV based I485 case. 
You would file to Chicago Lockbox they will forward it to corresponding local USCIS offic based on your address.
You can pay the DV fee right now.
We might not be able to tell about 13xxxx number which month it would be current based on 2013 it would only be currrent around 2014 august timeframe. But if it would follow the usual trend of DV then it would be current somewhere during december 2013.
You can go to the below link and check when it is current.
http://travel.state.gov/visa/bulletin/bulletin_1360.html