New drops of Crappy Dogecoin Doodles come every Monday. Unclaimed Doodles from the previous week are burned before each new drop.
Dogecoin came from Bitcoin. It's almost entirely Bitcoin code. I've always urged Dogecoin supporters to also respect and support Bitcoin, even if they prefer Dogecoin, but Dogecoin wouldn't exist without it.
I personally prefer Dogecoin. It has a dog on it.