I think what I primarily need to know is how did the F-State get dismantled,
In 2055 one of the many factions in the city was infiltrated by corporate agitators who managed to rally anti-anarchistic groups. Their discovery made it necessary for the corporations to speed up their plans. They got the AGS government to declare a state of emergency and authorise the corporate military to take control of the city. That lead to the division of Berlin into corporate West and anarchist East, where the anarchist forces managed to dug in. (A quaint detail: the wall was rebuilt.) The division lasted until 2072, when an attack with nanoweapons, likely a false-flag operation, gave the corporate forces another reason for an invasion of the East which they successfully pulled off this time around. Unfortunately for the corps the images from the military action didn't play well with the general populace and the dreaded stockpiles of nanoweapons were never found (amateurs). So instead of placing all of Berlin under corporate rule, the German government negotiated the creation of a representative government for Berlin and gave it the status of a free city. The Eastern "alternative" groups, being granted a one-time amnesty, became part of this system while maintaining self-government for their districts to some degree.
who controls what parts of the city, how the city is split up,
From the story you can infer that the division between East and West has more or less continued after the "second reunification". As I said the
Shadowhelix Berlin article has a current map:
http://shadowhelix.pegasus.de/Datei:%C3%9Cbersicht_Stadtteile_Berlin_Zugeh%C3%B6rigkeit.png
black - alternative, grey - so called "norm", gold - corporate
You can find the names of the districts on the other map in the Berlin article.
what day to day difficulty for runners is like there?
Don't know how to answer that. Probably not that different from other places?
What year is the 3rd edition sourcebook set in?
I'm not sure what is meant by "3rd edition Germany sourcebook" because the Germany Sourcebook (this is the only translated book) is 2nd edition. The year is 2054. Here on:
http://www.drivethrurpg.com/product/81899By the way, the German Berlin sourcebook is also available on DriveThruRPG. Maybe you want to have a look at the preview PDF. Actually, I hope it looks better for you because my standard pdf viewer does not seem to like it. Well at least there is a readable Liniennetzplan in it.
http://www.drivethrurpg.com/product/98529http://watermark.drivethrustuff.com/pdf_previews/98529-sample.pdf