Realized this earlier today. It explains why he looks the way he does, and why his physiology is so easily changed, but also why he can return to normal so easily as well. He also has access to things like portable holes, depending on the setting I'm playing him in, and how lax it is on logic in general.

As for his parents... I guess I'm technically his mom, since I conceived of the idea for him? Which would make the various characters that inspired him (Roger Rabbit, Bugs Bunny, The White Rabbit, etc) his many "fathers"? Eh, I'm not to worried about that end of it, personally speaking. It's just nice having a concrete explanation for something I'd just been doing for the heck of it up 'til now.