We have an all black cat similar to the cat in the first picture and she also likes to sit like that. Her new favorite is to sit with her back legs on the arm of the couch and her front legs on the end table like she is standing. I call it "stitting" cause she's not quite standing, not quite sitting.
When she's excited she does this thing with her front paws like she is digging. It's so funny!
My Apophis does the same thing. I call it "making biscuits". Somebody once told me that kittens who were weaned too soon do it a lot, but I can't confirm that.