OK I definitely think you have a few animals there that will only work if you have ES. All the frogs I believe you need ES for them to work properly. The black backed jackal I think was made from the wolf which is an ES animal. Same with the Arctic Fox. Also the Snow Tigers Christmas pack has a Siberian Husky in it which I also think was made from the wolf. The same goes for the dingo, as well. The caracal was made from the Spanish Lynx which also means it won't work for you, unfortunately. And the sorraia was made from P.Wild Horse which also came with ES. Finally, I think both of those Snow Tigers Easter packs have tour objects in them, which means they wouldn't work because the tour objects came with ES, when they introduced Jeep Tours and Sky Tram tours.
The rest of those downloads should work for you. The ones that I'm pretty sure I used when I just had the original ZT2 are the arabian oryx, king cheetah, asian elephant, yellow-eyed penguin, quagga, saola, siberian tiger, SWA, Sri Lankan Leopard, sumatran tiger, white tiger, and wooly rhino.
Basically any animal/object/etc. that was made from a model that came with ES is not going to be supported in your game. However I'm not sure why the ones that are supported aren't showing up for you. You may want to try removing all the unsupported downloads, and if that doesn't help, moving the .z2f files to the same directory where you're keeping the .dl files, as those are obviously being seen by the game.
Hope that helps!