When everything's cured, you're ready to de-mold. Just go around the seam between your two silicone halves and gently peel them apart. You're looking to get the soft Eco-Flex away from the harder Smooth-Sil at its own pace so it doesn't tear. Even though it looks like the quadruped is solid and robust, there's only 1/8" wall thickness between the surface and the wax cores and if you pull too quickly it might rip.
When you've got the entire part out, give it a once-over. Now's the easiest time to plug holes by adding some adhesive. If your wax has pushed up to the surface or you've got a big hole formed by a bubble in the mold, go ahead and brush some Sil-Poxy into the offending area. Make sure to extend a film of adhesive out from the site of the repair so its got lots of surface to grip. Even though Sil-Poxy is pretty strong once it's dried, it's not super sticky. If you put it on as if you were gluing a broken coffee cup back together, with adhesive only on the seam between the broken surfaces, it'll pop together pretty quickly. Get a little paintbrush and get glue deep into the hole, all up on the underside, and spread glue out on the surface.