Since you mentioned show tanks and marine specialists in your first post, I assume you have Marine Mania. The official Endangered Species Download Pack was created for those with Marine Mania. As for the pegasus of the Wild Wings pack, I extracted WWanimals_finalfix.ztd from the Wild Wings ".zip" and put WWanimals_finalfix.ztd in Zoo Tycoon's Updates folder. For those with CC, user downloads should go in the dlupdate folder. But for those without CC and without that folder, user downloads should go in the Updates folder. They should be put there manually and not from within the Zoo Tycoon program. When I went into Zoo Tycoon and started a Large Ocean freeform map, I did not have any problem finding the pegasus in the purchase menu. It was in the section for Grassland animals and is an animal from Europe. I did not have any problems creating a suitable exhibit for it. This testing was with Windows XP.
Because of the problems you are having, it appears something is not installed properly. You might need to uninstall Zoo Tycoon, delete the Zoo Tycoon folder, and reinstall Zoo Tycoon. Before doing so, you might want to save zoo.ini, any saved games, and any screenshots from the Zoo Tycoon folder. I assume you already have user downloads saved elsewhere. After reinstalling, you can then try to put in downloads 1 by 1 and test them. You might want to start with the simplest official downloads, since they were made to work with Marine Mania. When you install downloads, you should always do so manually and not from within Zoo Tycoon.
Good luck.