As for higher leveled adoptables, no. What's set up now is just a quick preview of what Sylonia's going to look like, and just to test the adoptables system i have in place. When i release the full site (ETA; still unknown) it might have "medals" (like on PokePlushies), and it will have shinies. Unfortunately, the shinies won't be out for some time, seeing as i need to figure out a way to make it so that adoptables under a certain level, and adoptables within a large percentage won't become shiny.
So, to answer your question, not yet. As for Gaia, i can't do it yet, but sometime in the near future is quite possible.