You will not find any luck convincing a rabbit to go for a walk like a dog :) They are about as obedient as a cat.

Rabbits (which ought to live indoors, away from cold, predators, and fright) are easily litter-box trained. You'll find that most at a shelter already are. (Our rabbit's habits are impeccable, though not all are.) The best litter is compressed wood pellets (e.g. wood stove pellets), which traps odor quite well. They will sometimes leave individual cocoa-puff-sized poops in strategic locations to mark their territory, but these are hard so they don't stain or smell.