Most of the walnut you get has been dried in a steam kiln. The steam dissolves some of the color and helps distribute it around in the wood more evenly, so it ends up being less interesting. Air-dried black walnut can have all sorts of interesting color variation.
I forgot to mention that walnut tends to be one of the easier woods to work with. It's hard enough to carve well, but not so hard as to be a chore. It's also one of the easiest woods to bend. All the walnut I've run into has been quite stable, too.
California 'claro' walnut is, I believe, English walnut grafted to American black walnut roots. It can have some wild grain due to the graft.
Curly grain black walnut is not too uncommon. Much of the walnut I get here in the States comes from Pennsylvania, where they hunt with shotguns. It's not unusual to find shot marks in the wood: bullet tracks with a pitch pocket at the end. The lead seems to dissolve fairly quickly: I've only ever found one piece of metallic lead in walnut. Often the walnut (and cherry) that has shot in it has some characteristic figure, which can be quite pronounced, and the wood will tend to be harder and denser as well. I call it 'enriched' walnut.