With what I read about World War 2, I come under the impression that the German Air Force was essentially gone by the time 1945 rolled around, to what extent was this true? Were there any German aircraft that participated in the Battle of Berlin and the months leading up to it?
There were some - JV 44 (Jagdverband 44) comes to mind. JV44 was basically a squadron made up of many of the top surviving German fighter aces. They flew Me 262 jet fighters and (according to an un-sourced wikipedia entry) "surviving records suggest the unit shot down approximately 47 Allied aircraft during April/May 1945."
The book "A Higher Call: An Incredible True Story of Combat and Chivalry in the War-Torn Skies of World War II" discusses in some detail the Luftwaffe's actions in the final months of the war from the perspective of a German Ace - its definitely worth a read for not only the amazing story the book is based on but just to see the German fighter pilots perspective (and you might just find yourself feeling a little uncomfortable when reading - if there was anyone fighting on the German side in WW2 that you can feel some sympathy with it has to be the fighter pilots trying to stop the allied bombers from raining high explosives on neighborhoods - intentionally or not)
Sources: http://en.wikipedia.org/wiki/Jagdverband_44 http://www.amazon.com/Higher-Call-Incredible-Chivalry-War-Torn/dp/0425252868
Which Battle of Berlin are you referring to? There were two. -There was a series of raids conducted by the RAF against Berlin which was a failure and the Battle of Berlin involving the Russians.
The US 8th Air Force set out to destroy the Luftwaffe as a fighting force in late 1943 and was incredibly successful with it. From what I have read, by the end of the war, the Luftwaffe had a large number of aeroplanes, but were hampered by a lack of pilots and a lack of fuel.
Up until the last days of the war, the Luftwaffe remained a threat to Allied bombers, with night fighters and attacks by Me-262s and Me-163s bringing down Allied bombers.