I have heard that you can't restock certain rarities if your account is young, also. I can't remember what age it was though, or where I heard it from...
But for your last question, the pound has this to say:
"WARNING!!! Pets that are above level 2, are limited-edition species, or that have been painted with certain rare or expensive paintbrushes, CANNOT be adopted by any account younger than four months. So be careful when abandoning a pet, if you're planning on trying to re-adopt it!"
So hopefully that helps ya