Wifi is available on the majority of ICE trains (>90%), but it is not guaranteed to work (so you won't get a rebate in case it does not work).
Also, Wifi is only available on certain tracks, as seen on this map.
Whether you get Internet on your trip also depends on the route that you are taking. A short search at bahn.de reveals that most likely you will take the ICE between Dusseldorf and Berlin (which has Wifi/Internet coverage) and take the Eurocity between Poznan and Berlin (which does not have Internet).
(2017 Edit:) Internet usage is free of charge in both first and second class. However, your connection speed will be reduced in second class if you generate more than 200 MB of traffic -- every device counts separately here and the counter is reset at the end of the day.
In terms of reliability, it is not bad. However, the connection will be frequently interrupted for short periods of times, which makes performing Voice-over-IP calls difficult.