I don't know about propaganda about the zoo in particular. I know it was well-regarded, but I there are many zoos in Europe and I've never read anything about the Nazis being terribly interested in conservation. Maybe someone else will know more.

The Berlin zoo was bombed repeatedly. The buildings were badly damaged. Some of the animals were killed outright, others escaped and had to be shot by the Germans. Others probably starved to death.

Late in the war, the Nazis built an anti-air tower near the zoo. It was one of the principal fortifications in the city--more of a complex than a mere tower. Thousands of civilians lived in it during the fighting with the red army. With that many hungry, desperate people around, you can imagine what might have happened to any surviving animals...

Animals Are My Life has a first hand account of a zoo bombing (but not in Berlin). It's pretty harrowing. Those poor elephants :(