I just started doing some barbarian fishing, but am I supposed to bank the fish or cut them up at the fishing spot?

Cut them up at the fishing spot.

And do i drop the roe/caviar?

Roe and caviar are stackable items, I believe.

Oooh, do the fishing spots even change

Just go with your rod, bait, and a knife. Catch full load, cut the fish. Cast rod, till your full again, drop your unused bait/fish cutlets and cut the fish again, now cast again and you'll use the roe/cavair as bait. Catch full load, cut, lather rinse, repeat. You never move at all unless spot moves.

Cool! This style rocks