OK, thanks for all the clues and other guesses. I might be a bit closer.
If 1 is indeed a jackrabbit, maybe the show is Samurai Jack or Jack Ryan?
2 could be a donkey, in which case I can think of Drop the Dead Donkey as a relevant link.
Is the takin going by Budorcas taxicolor, meaning "badger-coloured ox-antelope?" If so, might it be a reference to Bodger & Badger?
The rook could be a reference to Upstart Crow maybe?
I don't know where to start for the duiker, green magpie, and cichlid (or tilapia or just fish)