Not only are night droppings different in appearance than regular droppings, night droppings contain nutrients that the rabbit didn't digest the first time around. Rabbits usually eat night droppings, but occasionally you might find a few that your rabbit leaves behind. Generally, you don't need to worry about finding night droppings unless you find a lot of them. In that event, take your pet to the vet. You should take your pet to the vet as soon as possible.
Diarrhea can be symptomatic of a number of health problems.
This usually isn't anything to worry about. Once your rabbit urinates in the litter pan after you've changed the litter, he or she is less likely to hang out in the litter pan. If your rabbit isn't using the litter pan for urination, however, he or she might not have caught on to the litter pan's purpose. This will often happen with rabbits who aren't yet mature. Try using a second litter pan in the corner that your rabbit is now using for urination.