Since I seem to be the leader of these hybrid questions, I'LL TAKE THE CASE!
The entire story is probably fairly complicated, so I'll boil it down to the essentials:
Any mammal can have a child with another mammal. Predatory genetics typically are dominant, in other words, if you mix a cat with a dog, the dog would probably could out a bit more in the mix. Monkey and Tasmanian Devil? Probably more of the Devil. A Hedgehog and a Rabbit? ...your choice, since they'd typically walk right by each other
So, taking Shani's Goat/Bear example, it'd be possible if you really wanted to, but you'd probably end up having a bear with hooves for feet, and horns o.o Probably some goatish markings too, but it'd mostly be a bear since they're the predator.
Any reptile can have a child with another reptile. Again, predatory takes precedence, but not as much as on mammal side, so you can work a bit with it.
Avians can have a child with either reptile or mammal. They're sort of a molding building block between the two. This doesn't mean you can mix mammal and reptile by using an avian middle, it just means that they work with either. The reasoning being that Avians seem to have genetic background both from and to both mammals and reptiles, and partially the fact that avian features look fairly decent on either
Insects can't mix with Insects. If you wanted a butterfly cockroach, you couldn't at the moment, still need to talk with Kep about that
Though, I dunno who'd want that <.<
Artificial genetic mixing like with "Seven" is possible. Though keep in mind that, unless Kep decides otherwise, it has a high chance of failure. Seven came from a "family" of several hundred attempts, of which only a few matured, and she's the only one that ended up what they wanted from the experiment. Even then, she's mostly reptile, they were breeding for personality from the badger, mostly. Even the smallest changes like a personality rewrite can cause massive failure. Keep that in mind if you want to do something more drastic!
*waits for Kep to debunk anything* o.o;